SOLUTION: Translate into a system of equations: Burl is twice as old as son. Ten years ago, Burl was three times as old as his son. How old are they now?

Question 255598: Translate into a system of equations:
Burl is twice as old as son. Ten years ago, Burl was three times as old as his son. How old are they now?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
let b = burl's age.
let s = burl's son's age.

first equation is:

b = 2s

this means burl's age is equal to 2 times his son's age today.

second equation is:

b-10 = 3*(s-10)

this means burl's age 10 years ago was equal to 3 times his son's age 10 years ago.

your system of equations is:

b = 2*s
b-10 = 3*(s-10)

solve simultaneously by substitution.

take b = 2*s from first equation and substitute for b in second equation of:

b-10 = 3*(s-10) to get:

2*s - 10 = 3*(s-10).

simplify to get:

2*s - 10 = 3*s - 30

subtract 2*s from both sides of equation to get:

-10 = 3*s - 2*s - 30

add 30 to both sides of equation to get:

-10 + 30 = 3*s - 2*s

combine like terms to get:

20 = s

burl's son is 20 years old today.

burl must be 40 years old today (2*20 = 40).

ten years ago burl was 30.

ten years ago burl's son was 10.

30/10 = 3 means burl was 3 times as old as his son 10 years ago.

answer is:

burl is 40 years old today.
burl's son is 20 years old today.

RELATED QUESTIONS
A father is twice as old as his son. Ten years ago, the father was three times as old as... (answered by lwsshak3)

dr.kawasaki is twice as old as his son. twenty years ago, he was 4 times as old as his... (answered by mananth)

A father is twice as old as his son. Ten years ago he was three times as old as his son. (answered by ankor@dixie-net.com)

A father is twice as old as his son now. If he was three times as old as his son 10... (answered by JBarnum)

Peter is now twice as old as his som. Ten years ago, Peter was three times as his son.... (answered by josgarithmetic)

A father is three times as old as his son. Six years ago he was five times as old as his... (answered by Cromlix)

A man is twice as old as his son. Ten years ago, he was thrice as old as the son. what is (answered by LinnW)

ten years ago, a man was 3 times as old as his son. in 6 years, he will be twice as old... (answered by ptaylor)

A father is 27 years older than his son ten years ago he was twice as old as his son how... (answered by ikleyn,josgarithmetic)