SOLUTION: 2 years ago Paul was 7 times as old as Matt. 2 years from now, Paul will be 5 times as old is Matt. How old are Paul and Matt? I do have the answer, but can't come up with the co

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Question 159069This question is from textbook
: 2 years ago Paul was 7 times as old as Matt. 2 years from now, Paul will be 5 times as old is Matt. How old are Paul and Matt? I do have the answer, but can't come up with the correct equation.
TIA This question is from textbook

Found 2 solutions by KnightOwlTutor, gonzo:
Answer by KnightOwlTutor(293) (Show Source):
You can put this solution on YOUR website!
7(x-2)+4=5(X+2)
We are using Paul's age to calculate X.
There is a 4 year lapse between Matt's age two years ago and two years in the future. The age need to be equal.
7X-14+4=5X+10
Add -14+4=-10
subtract 5X from 7X
2X-10=10
Add ten to both sides
2X=20
X=10= Matt's current age
Two years ago Matt was 8
(7)(8)=56
56+2=58= Paul's current age
Double check
7(8)+4=(5)(12)
60=60

Answer by gonzo(654) (Show Source):
You can put this solution on YOUR website!
let P = paul's age now.
let M = Matt's age now.
2 years ago Paul was 7 times as old as Matt (was then is implied but not stated).
2 years ago Paul will be 5 times as old as Matt (will be then is implied but not stated).
equations become
P-2 = 7*(M-2) = 7*M - 14
P+2 = 5*(M+2) = 5*M + 10
adding 2 to both sides of the first equation and subtracting 2 from both sides of the second equation and they become
P = 7*M - 14 + 2 = 7*M - 12
P = 5*M + 10 - 2 = 5*M + 8
since they both equal the same thing they are equal to each other so they become
7*M - 12 = 5*M + 8
solving for M, equation becomes
2*M = 20
M = 10
substituting for M in the first equation gets
P = 7*M - 12
P = 7*10 - 12
P = 70 - 12
P = 58
substituting for P and M in the second equation gets
P = 5*M + 8
58 = 5*10 + 8
58 = 58
values for P and M are good.
answer is
P = 58
M = 10