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?

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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) About Me  (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.