Question 523800
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
:
:
Check this in the statement:
"Ten years ago he was five times his son's age."
60 - 10 = 5(20-10)
50 = 5(10); confirms out solutions