Question 159069
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