SOLUTION: My problem is: Walter is 43 years old; his daughter Paulette is 7. In how many years will Paulette be one-third of Walter's age? I'm afraid I don't know how to set it up.

Question 1039572: My problem is:
Walter is 43 years old; his daughter Paulette is 7. In how many years will Paulette be one-third of Walter's age?
I'm afraid I don't know how to set it up.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let
x = number of years that pass by

Walter is currently 43 years old. His daughter Paulette is currently 7 years old.

Present Ages
walter = 43
paulette = 7

If we fast foward x years into the future, this means
walter's age = 43+x
paulette's age = 7+x
simply add x to each value

We want to know when these future ages will be tied together through the following idea
(paulette's age) = (1/3)*(walter's age)

which is equivalent to saying
(walter's age) = (3)*(paulette's age)

So this means

(walter's age) = (3)*(paulette's age)

(43+x) = (3)*(7+x) ........ apply substitutions

43+x = 3*7+3*x

43+x = 21 + 3x

43+x-x = 21 + 3x-x

43 = 21 + 2x

43-21 = 21 + 2x-21

22 = 2x

2x = 22

2x/2 = 22/2

x = 11

So if 11 years pass by, then Walter will be 43+11 = 54 while Paulette will be 7+11 = 18. Notice how 18*3 = 54. Put another way, 18 is one-third of 54.

So the final answer is 11 years.
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