A man's age is three times his son's age.Ten years ago he was five times his son's age.

By forming two equations and solving them simultaneously,find both of their ages.

:

Let m = man's present age

let s = son's present age

:

Write an equation for each statement:

:

"A man's age is three times his son's age"

m = 3s

m - 3s = 0

:

"Ten years ago he was five times his son's age."

m - 10 = 5(s-10)

m - 10 = 5s - 50

m - 5s = -50 + 10

m - 5s = -40

multiply by -1 to change the signs, add to the first equation

-m + 5s = 40

+m - 3s = 0

------------adding eliminates m, find s

2s = 40

s = 40/2

s = 20 yr is the son's age

then

m = 3(20)

m = 60 is the man's age