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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