Question 572769: Sally is 40 years older than her son Peter. In 5 years she will be twice his age. How old are Sally and Peter? Make two solutions, one using a variable for Sally and one for Peter.
Answer by mathsmiles(68)   (Show Source):
You can put this solution on YOUR website! I understand everything except the last sentence. I'm going to proceed anyway and hope this helps you.
Sally's age now = S
Peter's age now = P
Sally's age 5 years from now = S + 5
Peter's age 5 years from now = P + 5
We also know a few facts:
S = P + 40 Sally is 40 years older than Peter
(S+5) = 2(P+5)
Let's use the first equation to substitute for Sally's age (S) in the second equation:
((P+40) + 5) = 2(P+5) Since the left side is all addition, we can remove the parens without a problem:
P + 40 + 5 = 2(P + 5)
P + 45 = 2(P + 5) Now multiply out the paren on the right:
P + 45 = 2P + 10 Subtract P from both sides:
45 = P + 10 Subtract 10 from both sides:
35 = P
Peter is 35. Since Sally is 40 years older than Peter, she is 75.
Checking our answer:
In 5 years, she'll be twice his age:
Peter will be 35 + 5 = 40 in 5 years.
Sally will be 75 + 5 = 80 in 5 years
Sally will be twice Peter's age. Correct!
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