SOLUTION: 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.

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!

RELATED QUESTIONS
Don is 5 years older than Peter is. In 5 years, Don will be twice as old as Peter is now. (answered by ikleyn)

John is twice as old as his friend Peter. Peter is 5 years older than Alice. In 5 years,... (answered by dpaulin,dmf30633)

james is twice as old as his friend peter. peter is 5 years older than alice right now.... (answered by Maths68)

Paul is Twice as old as his friend Peter. Peter is 5 years older than Mary. In 5 years,... (answered by ankor@dixie-net.com)

Geoffrey is twice as old as his friend Peter. Peter is 5 years older than Alice. In 5... (answered by stanbon,ikleyn)

John is twice as old as his friend Peter. Peter is 5 years older than Alice. In 5 years,... (answered by Maths68,japcaranza)

J-za is twice as old as his friend Peter. Peter is 5 years older than Alice. In 5 years,... (answered by josgarithmetic,ikleyn)

Sam is twice as old as her friend Peter. Peter is 7 years older than Alice. In 5 years,... (answered by ReadingBoosters)

Peter is forty years old and his son is ten years old. How long will it take so that will (answered by ikleyn,Alan3354)