Age Problem 5 Solution

This 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.

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..

X  and x -10

x + 7  and  x - 10 + 7  28  and 25 



(x+7)/2 + 10 = x - 3

x + 17 = 2x - 6  ******** Correction    2 * 10 = 20 + 7 = 27 So it should be

x + 27 = 2x - 6

x =33  ---> Which is Greg's age so Pol's is x-10 or 33 -10 = 23 

So Pol is 23 and Greg is 33

Work Problem 6 Solution

This 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?"

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
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.

multiply everything by 180 and get  2x + 30 + 3x = 180.

5x + 30 = 180
5x = 150
x = 30  So it would take 30 minutes if they worked together.   UPDATE:  "how long will it take them 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.

Plane Geometric Figure Problem 2 Solution

This 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?"

Since everything is relative to the 1st side make the 1st side x.

The 2nd side is 3x - 4 (4 less than 3 times the length of the 1st side)

and the 3rd side is x + 1 ( 1 more than the length of the 1st side) 

Now all the sides add up to 37 feet so set all this equal to 37.

x + 3x - 4  + x + 1 = 37

5x - 3 = 37

5x = 40 

x = 8

So the 1st side is 8 the 2nd side is 3(8) - 4 or 20 and the 3rd side is 9 .. 8 + 20 + 9 = 37

Finance Problem 2 Solution

This 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? "

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

So Alyssa will pay $497.25 for her mattress....

Coin Problem 6 Solution

This 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?"

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.  

So we have 20x + x = 231


21x = 231

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.

Number Problem 10 Solution

This is number problem 10 solution which read:

"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. "
 
ok 3 consecutive even integers would b x, x + 2, and x + 4

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

which is...  4x = (x+4)*2 + 12

4x = 2x + 8 + 12

2x = 20

x = 10  So the answer would be 10, 12, 14   to check  4(10)  =  (14)*2 + 12

40 = 28 + 12

40 = 40