This 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?"

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..

x + 12 = (3x + 12) / 2

2x + 24 = 3x + 12

x = 12

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.

## Tuesday, December 14, 2010

### Age Problem 6 Solution

## Thursday, November 25, 2010

### 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

## Tuesday, August 17, 2010

### Work Problem 5 Solution

This 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?

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.

So we got x/45 + x/90 + x/30 = 1 *Multiply both sides by 90 and get

2x + x + 3x = 90

6x = 90

x= 90/6 = 15

So it would take 15 minutes if all 3 worked together to finish the job.

## Tuesday, March 30, 2010

### Number Problem 9 Solution

This 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?"

So we have one number is x and another is 5 more than it which is x + 5. they equal 53.

So we have x + x + 5 = 53

2x + 5 = 53

2x = 48

x = 48/2 = 24 for one number and 24 + 5 or 29 for the other.

So check 24 + 29 = 53

53 = 53

## Friday, March 5, 2010

### Number Problem 8 Solution

This 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?"

Ok a number is x - the unknown

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

So we have (x + 16)/(x -12) = 1/3

Cross multiply and you get 3*(x + 16) = 1*(x - 12)

3x + 48 = x - 12

2x = - 60

x = -30

Check:

(-30 + 16)/(-30 - 12) =

-14/-42 = 14/ 42 = 1/3

## Saturday, January 23, 2010

### Finance Problem 1 Solution

This is the solution to the algebra finance word problem that An anonymous poster recently asked which read:

"An employee's new salary is $19,110 after getting a 5% raise. What was the salary before the increase in pay?"

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:

5% can be written 5/100

so,

5/100 * x + x = 105 multiply by 100

5 * x + 100x = 10500

5x + 100x = 10500

105x = 10500

x = 10500/105 = 100 so 100 is the answer you were looking for and it checks out..

You solve this problem exactly the same way.

5/100 * x + x = 19110 multiply by 100

5x + 100x = 1911000

105x = 1911000

1911000/105 = x

x = 18200 So check whats 5% of 18200 ? its 910 Now add 910 to 18200 and you get 19110. So it checks out.

## Sunday, January 10, 2010

### Time and Distance Problem 11 Solution

This is the answer to the algebra time and distance word problem #11 which was asked by another anonymous user on the "Algebra Word Problem Questions" post. The question read:

"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?"

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

For the algebra way you just set up the equation where you have :

20(3 + x) = 30x --> the time is x + 3 because she had a 3 hour head start

then you have 60 + 20x = 30x

60 = `10x

x = 60/10 = 6 --> 6 hours