tag:blogger.com,1999:blog-60781928466618221782016-05-20T01:23:13.364-07:00Algebra Word Problem SolutionsOn this blog you will find the answers to many different types of algebraic word problems including number, time and distance, mixture, finance, coin, age, lever, work, and plane geometric figure problems that I have problems set up for on another blog. I have a link to that blog below.Klitschko Fanhttp://www.blogger.com/profile/02473140486210939688noreply@blogger.comBlogger64125tag:blogger.com,1999:blog-6078192846661822178.post-36620251427302427902011-12-04T08:07:00.000-08:002011-12-04T08:07:25.714-08:00Plane Geometric Figure Problem 3 SolutionThis is the solution for the Algebra plane geometric figure problem as asked by an anonymous visitor which read, "catrina and tom want to buy a rug for a room that s 14 by 15 feet. They want to leave an even strip of flooring uncovered around the edges of the room. How wide a strip if they buy a rug with an area of 110 square feet?"<br /><br />It's easier to picture this. Draw a rectangle that's almost a square 14 x 15 feet. Within in draw another such figure but smaller. The space between that figure and the 14 x 15 figure is x. Now the smaller square has an area of 110 square feet. We now have an equation :<br /><br /><br />(15 -x ) (14 -x ) = 110<br /><br />210 + x^2 -14x - 15x = 110<br /><br />x^2 - 29x + 210 = 110<br /><br />x^2 -29x + 100 = 0<br /><br />(x - 25)(x - 4) = 0<br /><br />x = 4 or 25 however using 25 would result in negative dimensions which does not make sense. So 4 is the answer<br /><br />Check: (15 - 4) (14 - 4) = 110 = 11*10 = 110 Klitschko Fanhttp://www.blogger.com/profile/02473140486210939688noreply@blogger.com9tag:blogger.com,1999:blog-6078192846661822178.post-55013343791070330152011-12-03T15:46:00.000-08:002011-12-03T15:46:18.374-08:00Number Problem 14 SolutionThis is the solution for the Algebra number word problem which was asked by an anonymous visitor that read, "55 bowls of the same size capacity of food.<br />1. everyone gets their own bowl of soup<br />2. every two gets one bowl of spaghetti to share<br />3. every three will get one bowl of salad <br />4. all r required to have their own helping of salad, spaghetti, and soup."<br /><br />Ok you know the total number of people is x. Since '" every two gets one bowl of spaghetti to share" then x/2 of the people will have those bowls and since "every three will get one bowl of salad" then x/3 of the people will have those bowls in which they will total 55 bowls. <br />So we have:<br /><br />x + x/2 + x/3 = 55 ** multiply by 6<br /><br />6x + 3x + 2x = 330<br /><br />11x = 330<br /><br />x = 30<br /><br />So there are 30 bowls for soup, 30/2 = 15 bowls for spaghetti , and 30/3 = 10 bowls for salad. <br /><br />Check 30 + 15 + 10 = 55Klitschko Fanhttp://www.blogger.com/profile/02473140486210939688noreply@blogger.com1tag:blogger.com,1999:blog-6078192846661822178.post-34213970530277179692011-12-03T14:37:00.000-08:002011-12-03T14:37:32.366-08:00Finance Problem 4 SolutionThis is the solution to the Algebra finance word problem a anonymous user asked, "An administrative assistant orders cellular phones for people in her department. The brand A phones cost $89.95 and the brand b phones $34.95.If she ordered 3 times as many brand b phones as brand a phones at a total cost of $584.40, how many of each did she order?"<br /><br />Ok to make things easier lets make it cents. Just remember to divide by 100 when done to get the answer in dollars and cents...<br /><br />So brand A is 8995 and b is 3495 which had 3 times as many sold as a and all the combinations of phones totalled 58440. <br /><br />So 8995x + 3495(3x) = 58440<br /><br />8995x + 10485x = 58440<br /><br />19480x = 58440<br /><br />x = 3 So there were 3 brand A's and 3(3) = 9 brand B's sold.Klitschko Fanhttp://www.blogger.com/profile/02473140486210939688noreply@blogger.com1tag:blogger.com,1999:blog-6078192846661822178.post-46876819020751527172011-12-03T14:29:00.000-08:002011-12-03T14:37:58.165-08:00Finance Problem 3 SolutionThis is the solution to the Algebra finance word problem asked by an anonymous user which read, "Alex has made 42 of the 48 payments he owes on his car but is having trouble continuing to make the payment in full. He has made an arrangement with the bank to pay 2/3rds of his monthly payment, rather than the entire payment, every month. How many months will it take Alex to pay off his car loan with this new payment arrangement?"<br /><br />Ok, 1st find the remaining months : 48 - 42 = 6 So there are 6 months at full payments. But, you are no longer doing full payments you are doing 2/3s of a payment. So 2/3 of what would equal out 6 ? Or<br /><br />2x/3 = 6<br /><br />2x = 18<br /><br />x = 18/2 = 9 .. So it will take Alex 9 months to pay off his car loan with the new payment arrangement..Klitschko Fanhttp://www.blogger.com/profile/02473140486210939688noreply@blogger.com0tag:blogger.com,1999:blog-6078192846661822178.post-36809247053402833392011-10-21T17:30:00.000-07:002011-10-21T17:30:58.426-07:00Number Problem 13 SolutionThis is the solution to algebra number problem 13 as asked by an anonymous user: "A maths test contains 10 questions. Ten points are given for each correct answer and three points deducted for an incorrect answer. If Ralph scored 61, how many did he get correct?"<br /><br />Ok on this problem you can come up with a solution faster by just quick trial an error. You know that if it only counts 3 points off for each wrong answer and they got a 61 then they had to have at least a 70 before the points were taken off. If they got a 70 that means they missed 3 problems (3 * 3 = 9) 70 - 9 = 61 . So the answer is they got 7 problems right and 3 wrong.<br /><br />Now to set this up using algebra...<br /><br />10x - 3(10-x) = 61 You are subtracting the wrong answers worth 3 points a piece from the right ones worth 10 a piece. You don't know how many of each so you are saying there are x amount of 10 valued answers and (10 - x) number of 3 valued wrong answers. <br /><br />10x - (30 - 3x) = 61<br /><br />10x -30 + 3x = 61<br /><br />13x = 91 --> x = 91/13 = 7 --> so there are 7 right 10 valued problems and (10-7) or 3 wrong 3 point negative value ones.....<br /><br />You could have also set it up like this 10(10 - x) - 3x = 61 and got the same answer....Klitschko Fanhttp://www.blogger.com/profile/02473140486210939688noreply@blogger.com1tag:blogger.com,1999:blog-6078192846661822178.post-24814578301602534892011-10-21T17:21:00.000-07:002011-10-21T17:21:43.431-07:00Age Problem 8 SolutionThis is the solution to the algebra age problem asked by Joshua that read, "A man is 4 years older than his wife and 5 times as old as his son. When the son was born, the age of the wife was six-sevenths that of her husband's age. Find the age of each."<br />Ok so here we go...<br /><br />"A man is 4 years older than his wife"<br />m = w + 4<br />Now we will subtract 4 from both sides to use this conveniently later ( you will see)<br />w = (m-4)<br /><br />"and 5 times as old as his son."<br />m = 5s<br /><br />"When the son was born, the age of the wife was six-sevenths that of her husband's age."<br />w - s = 6/7(m-s)<br /><br />7(w-s) = 6(m-s) --><br />7w - 7s = 6m - 6s ---><br />7w = 6m - 6s + 7s ---><br />7w = 6m + s<br />replace w with (m-4)<br />7(m-4) = 6m + s<br />7m - 28 = 6m + s<br />7m - 6m = s + 28<br />m = s + 28<br />replace m with 5s<br />5s = s + 28<br />5s - s = 28<br />4s = 28<br />s = 7 yrs is the son's age<br />then<br />5(7) = 35 yrs is Dad's age<br />and<br />35-4 = 31 yrs is Mom's age<br /><br />Now check work...<br />"When the son was born, the age of the wife was six-sevenths that of her husband's age."<br />31 - 7 = 6/7(35 - 7)<br />24 = 6/7*28<br />24 = 24;Klitschko Fanhttp://www.blogger.com/profile/02473140486210939688noreply@blogger.com1tag:blogger.com,1999:blog-6078192846661822178.post-42860058649545103072011-10-09T17:43:00.000-07:002011-10-09T17:43:31.392-07:00Number Problem 12 SolutionThis is the solution to a number algebra word problem that was asked by<span dir="ltr"></span> Zakeus who said , "The numerator and denominator of a fraction are together equal to 100. Increase the numerator by 18 and decrease the denominator by 16 and the fraction is doubled. What is the fraction?"<br /><br /><br />Ok you want to set up 2 equations the 1st one is easy. x + y = 100 so y = 100 - x<br /><br />The other would be (x + 18)/(y - 16) = (x/y)*2<br /><br />(x + 18) y = 2x (y - 16) Now substitute 100-x for y....<br /><br />(x + 18)(100 - x) = 2x(100 - x - 16)<br /><br />100 x + 1800 - x^2 -18x = 2x(84-x)<br /><br />82x + 1800 -x^2 = 168x - 2x^2 Now combine like terms...<br /><br />x^2 - 86x + 1800 = 0 <br /><br />(x - 50)(x - 36) = 0 Now 50/50 is 1 and that's not the fraction we are looking for ( y = 100 - 50 = 50)<br /><br />So substituting 36 in for x we have y = 100 - 36 = 64 So the fraction is 36/64 Now to verify this is correct add 18 to the numerator and subtract 16 from the denominator and we get ..<br /><br />54/48 ... Ok now to verify if this is double the other equation lets reduce the equations. 36/64 4 is the gcd so we get 9/16 and for 54/48 , 3 is the gcd and we get 18/16 and 9/16 * 2 does equal 18/16, so we have the correct answer....Klitschko Fanhttp://www.blogger.com/profile/02473140486210939688noreply@blogger.com0tag:blogger.com,1999:blog-6078192846661822178.post-27817040348402755462011-10-09T09:59:00.000-07:002011-10-09T09:59:30.583-07:00Time and Distance Problem 13 SolutionThis is the solution for a algebra time and distance word problem asked by a anonymous user: "Two trains left a station at the same time. One traveled north at a certain speed and the other traveled south at twice that speed. After 3 hours , the trains were 400 miles apart. How fast was each train traveling?"<br /><br /><br />The speed of the 1st train is x and the 2nd train is twice that or 2x. Ok the trick here is lets say someone is going 50 mph north and the other person is going twice that 100 the opposite direction. This distance separating them would be the same thing as if you added their speeds and it was going one direction -- in other words if someone was just going 150mph they would cover the same ground. Also rate multiplied by time equals distance. We know the time is 3 hours and the distance is 400. So<br /><br />(x + 2x) (3) = 400<br /><br />3x(3) = 400<br /><br />9x = 400<br /><br />x = 400/9 = 44 and 4/9ths mph is the 1st train and 88 and 8/9ths (800/9) mph is the 2nd train.Klitschko Fanhttp://www.blogger.com/profile/02473140486210939688noreply@blogger.com0tag:blogger.com,1999:blog-6078192846661822178.post-85695172546848501172011-10-09T09:41:00.000-07:002011-10-09T09:41:18.079-07:00Age Problem 7 SolutionThis is the solution to a algebra age word problem as asked by a anonymous user: "Nona is one-third as old as her mother. Five years ago, she was only one-fifth of the age of her mother. How old is Nona now? "<br /><br /><br />It is easier to set this up with two unknowns say x and y and have 2 equations.<br /><br />The 1st equation would be: x = 1/3(y) or x = y/3 since Nona is currently 1/3 as old as her mother. Now 5 years ago she was only 1/5th the mothers age so the other equation would be..<br /><br />x -5 = 1/5(y - 5) multiply by 5..<br /><br />5x - 25 = y - 5 so<br /><br />y = 5x - 20 .. plug this back into the 1st equation and you get..<br /><br />x = (5x - 20)/3 - -multiply by 3<br /><br />3x = 5x - 20 so 2x = 20 and x = 10<br /><br />So Nona is 10 years old currently and the mom is 30. To check this go 5 years back... Nona would be 5 and the mother would be 25 ------ 5/25 = 1/5ths of her mothers age...Klitschko Fanhttp://www.blogger.com/profile/02473140486210939688noreply@blogger.com0tag:blogger.com,1999:blog-6078192846661822178.post-14093134491421902392011-10-09T09:13:00.000-07:002011-10-09T09:13:33.307-07:00Mixture Problem 7 SolutionThis is the solution to a new algebra mixture problem as asked by Califax who asked, "A 50-lb solution of acid and water is 20% (by weight). How much pure acid must be added to this solution to make it 30% acid?"<br /><br />1/5 = 20 % ..... 3/10 = 30 % x = the unknown amount in lbs we want to add of 100% or 1/1 or 1 or just x of pure acid.<br /><br />50(1/5) + x = 3/10 (50 + x) multiply by 10...<br /><br />100 + 10x = 3(50 + x)<br /><br />100 + 10x = 150 + 3x<br /><br />7x = 50 = 50/7 = 7 and 1/7th lbs of pure acid needs to be added to make the solution 30% acid.Klitschko Fanhttp://www.blogger.com/profile/02473140486210939688noreply@blogger.com1tag:blogger.com,1999:blog-6078192846661822178.post-65253781779189753002011-10-07T12:32:00.000-07:002011-10-07T12:32:54.199-07:00Number Problem 11 SolutionThis is a new problem as asked by a anonymous visitor which read: "a number added to five times its reciprocal is -6. find the number "<br /><br />Ok non-algebraically you can think of what numbers added together will make 6(of course they will be negative to make negative 6) --- 1 and 5 and 4 and 2 , and 6 and 0... You can't have a reciprocal of 0 and a reciprocal of 6 : 1/6 when multiplied by 5 makes 5/6ths and you know those added together : -6 + - 5/6ths dont make -6. Same thing goes for 2 and 3 --> 2 + 5/2 or 3 + 5/3 dont make 6. 1 and 5 however do work. The reciprocal of 1 is 1 so 1 + 5/1 =6 and so does 5 + 5/5 = 6 (Of course negative again). So there are 2 answers -1 and -5...<br /><br />Algebraically... -x + (1/-x)5 = -6 =<br /><br />-x -5/x = -6 (multiply by -x)<br /><br />x^2 + 5 = 6x<br /><br />x^2 + 6x + 5 = 0<br /><br />(x + 1) (x + 5 ) = 0 <br /><br />So the answers are x = -1 and -5Klitschko Fanhttp://www.blogger.com/profile/02473140486210939688noreply@blogger.com1tag:blogger.com,1999:blog-6078192846661822178.post-5940306154044747772010-12-14T11:57:00.000-08:002010-12-14T11:57:29.976-08:00Age Problem 6 SolutionThis is the answer to the age algebra word problem that asked, "Bob is one third the age of his father. In 12 years he will be half the age of his father. How old is each now?"<br /><br /><br />Ok Bob being 1/3 the age of his father is the same thing as saying the father is 3 times as old as him. It makes it easier to work with. So let Bob be x and his father be 3x. And in 12 years bob will be half as old as his father. So we have..<br /><br /><br />x + 12 = (3x + 12) / 2<br /><br />2x + 24 = 3x + 12<br /><br />x = 12<br /><br /><br />So Bob is 12 years old and his father is 3(12) or 36 years old now. In 12 years Bob will be 12 + 12 or 24 years old and his father will be 36 + 12 or 48 years old which means Bob will be half as old so it checks out.Klitschko Fanhttp://www.blogger.com/profile/02473140486210939688noreply@blogger.com17tag:blogger.com,1999:blog-6078192846661822178.post-44436305392648173152010-11-25T22:49:00.000-08:002011-10-23T15:35:33.422-07:00Age Problem 5 SolutionThis is the algebra age word problem that read Pol is 10 years younger than greg. In 7 years, he will be 10 years more than one halfas old as greg. Find their age at present. help me solve it.<br /><br />Let Greg be X and Pol be X - 10 as far as current ages. In 7 years (thats x + 7) he will be 10 years more than 1/2 as old as greg (thats (x - 10 + 10)/2 or x/2). So set them equal..<br /><br />X and x -10<br /><br />x + 7 and x - 10 + 7 28 and 25 <br /><br /><br /><br />(x+7)/2 + 10 = x - 3<br /><br />x + 17 = 2x - 6 ******** Correction 2 * 10 = 20 + 7 = 27 So it should be<br /><br />x + 27 = 2x - 6<br /><br />x =33 ---> Which is Greg's age so Pol's is x-10 or 33 -10 = 23 <br /><br />So Pol is 23 and Greg is 33Klitschko Fanhttp://www.blogger.com/profile/02473140486210939688noreply@blogger.com16tag:blogger.com,1999:blog-6078192846661822178.post-43642632471181409302010-11-25T14:31:00.000-08:002011-12-01T01:09:43.836-08:00Work Problem 6 SolutionThis is the solution to Work Problem 6 which asked, "A mother can rake a yard in 90 minutes and her daughter can do it in 60 minutes.If the mother rakes for 15 minutes before her daughter joins her,how long will it take them to finish the work?"<br /><br />Ok the mother can do 1/90th of her job in a minute so if you have x/90 in 90 minutes 90/90 = 1 she completes her job same thing goes for the the daughter .. 1/60 of her job done in a minute with x/60 in 60 minutes 60/60 = 1 she completes her job. Seems kind of silly that I'm pointing this out but this is how you solve the problem you just add their work together and set it equal to 1. Their is one additional stipulation in the problem though and thats the mother starting 15 minutes before the daughter joins the mother otherwise it would just be<br />x/90 + x/60 = 1... but the mother rakes for 15 minutes and completes 15/90 of her job so the way to write it out would be x/90 + 15/90 + x/60 = 1.<br /><br />multiply everything by 180 and get 2x + 30 + 3x = 180.<br /><br />5x + 30 = 180<br />5x = 150<br />x = 30 So it would take 30 minutes if they worked together. <b>UPDATE</b>: "how long will it take <b>them</b> to finish the work?" <-- Sounds to me like how long will they finish together thus 30 minutes the answer. But if you want to take this to mean how long did it take them to finish the total job then add the 15 minutes of initial work done by the mother which would be 30 + 15 = 45.Klitschko Fanhttp://www.blogger.com/profile/02473140486210939688noreply@blogger.com20tag:blogger.com,1999:blog-6078192846661822178.post-44661097420351613582010-11-25T14:09:00.000-08:002010-11-25T14:09:57.131-08:00Plane Geometric Figure Problem 2 SolutionThis is the Plane Geometric Figure Problem 2 Solution which asked "The length of the second side of a triangle is four less than three times the length of the first side. The length of the third side is one more than the length of the first side. If the perimeter of the triangle is 37 feet, what is the length of the first side?"<br /><br />Since everything is relative to the 1st side make the 1st side x.<br /><br />The 2nd side is 3x - 4 (4 less than 3 times the length of the 1st side)<br /><br />and the 3rd side is x + 1 ( 1 more than the length of the 1st side) <br /><br />Now all the sides add up to 37 feet so set all this equal to 37.<br /><br />x + 3x - 4 + x + 1 = 37<br /><br />5x - 3 = 37<br /><br />5x = 40 <br /><br />x = 8<br /><br />So the 1st side is 8 the 2nd side is 3(8) - 4 or 20 and the 3rd side is 9 .. 8 + 20 + 9 = 37Klitschko Fanhttp://www.blogger.com/profile/02473140486210939688noreply@blogger.com1tag:blogger.com,1999:blog-6078192846661822178.post-28580575518756832392010-11-25T13:50:00.000-08:002010-11-25T13:50:25.606-08:00Finance Problem 2 SolutionThis is the finance problem 2 solution which read: "A local furniture store is selling all $850 mattresses at 35% off. Alyssa is buying a mattress and has a coupon for an additional 10% off the sale price. What will Alyssa pay for her mattress? "<br /><br />Ok you just have to take the discount off twice. 35% off of $850 would be $297.50 so 850 - 297.50 = $552.50 is the sale price. Now she has a coupon for another 10% off that sales price. So 10% of 552.50 is 55.25 and 552.50 - 55.25 = 497.25<br /><br />So Alyssa will pay $497.25 for her mattress....Klitschko Fanhttp://www.blogger.com/profile/02473140486210939688noreply@blogger.com0tag:blogger.com,1999:blog-6078192846661822178.post-78420023900485549042010-11-25T13:41:00.000-08:002010-11-25T13:41:34.246-08:00Coin Problem 6 SolutionThis is the coin problem 6 solution which read "a stack of pennies and dimes has a total value of $2.31. how many dimes are in the stack if there are twice as many dimes as pennies?"<br /><br />make $2.31 into cents so 231 cents .. a dime is worth 10x and penny is worth x. So if you had 1 dime and 1 penny you would have 10(1) or 10 cents plus 1(1) or 1 cent which is 11 cents. Were trying to have it add up to 231 cents though and there are twice as many dimes 2(10x) or 20x as pennies. <br /><br />So we have 20x + x = 231<br /><br /><br />21x = 231<br /><br />x = 11 So there are 11 penny's or 11 cents and 22 dimes or 220 cents .. 220 cents plus 11 cents equals 231 cents or $2.31.Klitschko Fanhttp://www.blogger.com/profile/02473140486210939688noreply@blogger.com0tag:blogger.com,1999:blog-6078192846661822178.post-11086024781474124212010-11-25T13:25:00.000-08:002010-11-25T13:25:24.831-08:00Number Problem 10 SolutionThis is number problem 10 solution which read: <br /><br />"Find 3 consecutive even integers such that 4 times the first is decreased by the second is 12 more than twice the third. " Ok I'm not understading the "is decreased by the" part so I assume it was a typo and you just meant "Find 3 consecutive even integers such that 4 times the first is 12 more than twice the third. "<br /> <br />ok 3 consecutive even integers would b x, x + 2, and x + 4<br /><br />4 times the 1st would be just 4x and is equal to 12 more than twice the 3rd which would be (x + 4) * 2 + 12<br /><br />which is... 4x = (x+4)*2 + 12<br /><br />4x = 2x + 8 + 12<br /><br />2x = 20<br /><br />x = 10 So the answer would be 10, 12, 14 to check 4(10) = (14)*2 + 12<br /><br />40 = 28 + 12<br /><br />40 = 40Klitschko Fanhttp://www.blogger.com/profile/02473140486210939688noreply@blogger.com13tag:blogger.com,1999:blog-6078192846661822178.post-38119277689977732512010-08-17T13:21:00.000-07:002010-08-17T13:21:23.719-07:00Work Problem 5 SolutionThis is the solution to the work problem # 5 which read: Jim can fill a pool carrying buckets of water in 30 minutes. Sue can do the same job in 45 minutes. Tony can do the same job in 1 ½ hours. How quickly can all three fill the pool together?<br /><br /><br /><br />Ok Tony takes 1 and 1/2 hours which is 90 minutes, and then we got jim at 30 minutes and Sue at 45 minutes. Convert everything to find out how much each can do in 1 minute. Tony does 1/90 th of his job in 1 minute Jim 1/30 th and Sue 1/45 th. So lets take just one individual persons job say Sue for example. If someone says Sue takes how long to finish her job if you know that she can do 1/45 of her job in a minute what would u say? 45 minutes. Or you can look at it as x/45 = 1 which means how many over 45 would = 1? The answer of course would be 45 again. So we set this problem up just like that only were ADDING the other peoples jobs together and setting it equal to 1.<br /><br />So we got x/45 + x/90 + x/30 = 1 *Multiply both sides by 90 and get<br /><br />2x + x + 3x = 90<br /><br />6x = 90<br /><br />x= 90/6 = 15 <br /><br />So it would take 15 minutes if all 3 worked together to finish the job.Klitschko Fanhttp://www.blogger.com/profile/02473140486210939688noreply@blogger.com2tag:blogger.com,1999:blog-6078192846661822178.post-76224560303184327862010-03-30T16:37:00.000-07:002010-03-30T16:50:45.940-07:00Number Problem 9 SolutionThis is the solution to the algebra number word problem which was asked by a anonymous person in the ask question section which read, "One number is 5 more than another.their sum is 53.what are the two numbers?"<br /><br /><br />So we have one number is x and another is 5 more than it which is x + 5. they equal 53.<br /><br />So we have x + x + 5 = 53<br /><br />2x + 5 = 53<br /><br />2x = 48<br /><br />x = 48/2 = 24 for one number and 24 + 5 or 29 for the other.<br /><br />So check 24 + 29 = 53<br /><br />53 = 53Klitschko Fanhttp://www.blogger.com/profile/02473140486210939688noreply@blogger.com2tag:blogger.com,1999:blog-6078192846661822178.post-60312869312486352882010-03-05T12:13:00.001-08:002010-03-05T12:25:55.722-08:00Number Problem 8 SolutionThis is the solution to the Algebra Number word problem # 8 which read "The ratio of 16 more than a number to 12 less than that number is 1 to 3. What is the number?"<br /><br /><br /><br />Ok a number is x - the unknown<br /><br />The problem says that ration of 16 more than a number --> which is x + 16 to 12 less than that number(the number is still x) or x - 12 is 1 to 3<br /><br />So we have (x + 16)/(x -12) = 1/3<br />Cross multiply and you get 3*(x + 16) = 1*(x - 12)<br /><br />3x + 48 = x - 12<br /><br />2x = - 60<br /><br />x = -30<br /><br />Check:<br />(-30 + 16)/(-30 - 12) =<br />-14/-42 = 14/ 42 = 1/3Klitschko Fanhttp://www.blogger.com/profile/02473140486210939688noreply@blogger.com0tag:blogger.com,1999:blog-6078192846661822178.post-71656737480039895302010-01-23T19:14:00.000-08:002010-01-23T19:23:48.766-08:00Finance Problem 1 SolutionThis is the solution to the algebra finance word problem that An anonymous poster recently asked which read:<br /><br />"An employee's new salary is $19,110 after getting a 5% raise. What was the salary before the increase in pay?"<br /><br />Ok easiest way to think about this is try something you do know for sure. Whats 5% of 100? 5 right--- Ok, so what if the problem said an employee's new salary was $105 after a 5% increase in pay what was the salary before... Ok you already know the answer 100.... So how would u come up with the new total? Well 5% of 100 is 5 and then you add it to the original amount of 100 which makes 105. So, you set up your problem like that:<br /><br />5% can be written 5/100<br /><br />so,<br /><br />5/100 * x + x = 105 multiply by 100<br /><br />5 * x + 100x = 10500<br /><br />5x + 100x = 10500<br /><br />105x = 10500<br />x = 10500/105 = 100 so 100 is the answer you were looking for and it checks out..<br /><br />You solve this problem exactly the same way.<br /><br />5/100 * x + x = 19110 multiply by 100<br /><br />5x + 100x = 1911000<br /><br />105x = 1911000<br /><br />1911000/105 = x<br /><br />x = 18200 So check whats 5% of 18200 ? its 910 Now add 910 to 18200 and you get 19110. So it checks out. <br /><br /><br /><br /><br /><div class="tag_list">Tags: <span class="tags"><a href="http://technorati.com/tag/Finance+Problem+Solutions" rel="tag">Finance Problem Solutions</a>, <a href="http://technorati.com/tag/Algebra+word+problems" rel="tag">Algebra word problems</a>, <a href="http://technorati.com/tag/algebra+word+problem+solutions" rel="tag">algebra word problem solutions</a></span></div>Klitschko Fanhttp://www.blogger.com/profile/02473140486210939688noreply@blogger.com4tag:blogger.com,1999:blog-6078192846661822178.post-48642766063817489502010-01-10T16:50:00.000-08:002010-01-10T16:57:45.763-08:00Time and Distance Problem 11 SolutionThis is the answer to the algebra time and distance word problem #11 which was asked by another anonymous user on the "<a href="http://algebra-word-problems.blogspot.com/2009/08/algebra-word-problem-questions.html">Algebra Word Problem Questions</a>" post. The question read:<br /><br />"Alexis left Miami and drove at a speed of 20 kph. Thomas left 3 hours later, from the same point, and drove at a speed of 30 kph. How long will it take Thomas to catch up to Alexis?"<br /><br /><br />Ok non-algebraically the easiest way to figure this one out is to figure how far kilometers Alexis has gone before Thomas even leaves. Since Thomas left 3 hours later and Alexis drove 20 kph then Alexis has gone 20(3) or 60 k or kilometers. Thomas is going faster but how much faster than Alexis? (30 - 20)kmh = 10 So, the question is if he's creeping up at 10 kmh how long would it take him to go the distance that Alexis is ahead which we figured out to be 60 kilometers. Well at 10 kph it would take 6 hours to to 60 k... 60 k / 10 kph = 6 h<br /><br />For the algebra way you just set up the equation where you have :<br /><br />20(3 + x) = 30x --> the time is x + 3 because she had a 3 hour head start<br /><br />then you have 60 + 20x = 30x<br /><br />60 = `10x <br /><br />x = 60/10 = 6 --> 6 hours<br /><br /><br /><br /><br /><br /><div class="tag_list">Tags: <span class="tags"><a href="http://technorati.com/tag/Time+and+Distance+Problem+Solutions" rel="tag">Time and Distance Problem Solutions</a>, <a href="http://technorati.com/tag/algebra+word+problem+solutions" rel="tag">algebra word problem solutions</a></span></div>Klitschko Fanhttp://www.blogger.com/profile/02473140486210939688noreply@blogger.com1tag:blogger.com,1999:blog-6078192846661822178.post-48041488283435799322009-11-14T15:54:00.000-08:002009-11-23T20:18:45.442-08:00Work Problem 4 SolutionThis is the solution to the algebra work word problem # 4 which read: "Joe and Jim paint a house. Joe can paint it alone in 5 days, Jim in 8 days. They start to paint it together but after 2 days Jim stops. How long will Joe finish it alone?"<br /><br />Joe takes 5 days<br />Jim 8 <br />to paint a house<br /><br />So Joe can do 1/5 of his job in one day and Jim can do 1/8th of his job in 1 day. If you just take Joe for example you can see where I'm heading on solving this problem. Joe can do 1/5th of his job in one day. So how long would he finish his job -- well besides knowing the answer already -- you would set it up as x/5 = 1. 1 being when the job is complete not just a "fraction" of his work being done. So the answer is 5 of course 5/5 = 1. You use this exact same method to solve the problem for both Joe and Jim.<br /><br />**********Correction************ I realized I solved the problem before if they both continued working the job, but this problem states JIM stops working in 2 days. So Joe does x/5 part of his job in 2 days? 2/5 and Jim does x/8 part of his job in 2 days? 2/8, and Joe keeps working. So the equation would be<br /><br />2/5 + 2/8 + x/5 = 1 multiply by 40 and get<br />16 + 10 + 8x = 40<br /><br />26 + 8x = 40<br />8x = 40 - 26<br />8x = 14<br />x = 14/8 or 1 and 3/4ths so it would take 1 and 3/4ths days more for Joe to finish the job alone..<br /><br /><br /><div class="tag_list">Tags: <span class="tags"><a href="http://technorati.com/tag/Work+Problem+Solutions" rel="tag">Work Problem Solutions</a>, <a href="http://technorati.com/tag/algebra+word+problem+solutions" rel="tag">algebra word problem solutions</a></span></div>Klitschko Fanhttp://www.blogger.com/profile/02473140486210939688noreply@blogger.com11tag:blogger.com,1999:blog-6078192846661822178.post-43269514700743143412009-10-07T09:10:00.000-07:002009-10-07T09:20:37.856-07:00Mixture Problem # 6 SolutionThis is the solution to the algebra mixture word problem # 7 which read:<br /><br />"If a merchant has two types of tea, one worth $2.70 per kilogram and the other worth $3.00 per kilogram, how many kilograms of each type should the merchant use in order to produce 30 kilograms of a blend that is worth $2.95 per kilogram?"<br /><br />Even though this involves money we treat it like a mixture problem. <br /><br />You got to unknowns but if you look at it as having x = 1 amount and y = 30 -x then you just have x, and 30 -x so...<br /><br />Its the x amount * the 270 cent worth tea plus the 30 - x amount * the 300 cent worth tea is going to equal 30 * 295 cent blend<br /><br />270 * x + 300(30-x) = 30(295)<br /><br />270x + 9000 - 300x = 8850 <br /><br />-30x = -150<br /><br />30x = 150<br /><br />x = 150/30 = 5<br /><br />so 5 kilograms of the 270 cent or $2.70 tea and 30 -5 or 25 kilograms of the 300 cent or $3.00 tea would need to be mixed together to make 30 kilograms of the $2.95 cent tea.<br /><br />check 270 * 5 + 300 * 25 = 30*295<br /><br />1350 + 7500 = 8850<br />8850 = 8850<br /><br /><br /><br /><br /><br /><div class="tag_list">Tags: <span class="tags"><a href="http://technorati.com/tag/Mixture+Problem+Solutions" rel="tag">Mixture Problem Solutions</a>, <a href="http://technorati.com/tag/algebra+word+problem+solutions" rel="tag">algebra word problem solutions</a></span></div>Klitschko Fanhttp://www.blogger.com/profile/02473140486210939688noreply@blogger.com1