Academic Subjects
➤
Math
➤
Algebra ➤
Algebraic Equations ➤
Ten Years Ago Anna Was Twice As Old As Charlie

Ten years ago, Anna was twice as old as Charlie
3 years ago, 4 times Megans age was 3 times Charlies age today
In 15 years, Anna is 8 years older than Megan
How old are Anna, Megan & Charlie?



Let's take this step by step

Ten years ago, Anna was twice as old as Charlie

Ten years ago
A - 10 = C - 10
Anna was twice Charlies age, so we multiply Charlies age by 2
A - 10 = 2(C - 10)


3 years ago, 4 times Megans age was 3 times Charlies age today

4 times Megans age was 3 times Charlies age
4M = 3C
and that was Megans age 3 years ago
4M - 3 = 3C


in 15 years, Anna is 8 years older than Megan
A + 15 = M + 15 + 8


This leaves us with three equations

A - 10 = 2(C - 10)
4M - 3 = 3C
A + 15 = M + 15 + 8

Rearranging these, we'll get

A - 2C = - 10
4M - 3C = 3
A - M = 8



Now, we treat these as a system of equations

A - M = 8
- A + 2C = 10 / - M + 2C = 18


4(- M + 2C = 18)

- 4M + 8C = 72
+ 4M - 3C = 3 / 5C = 75


If 5C = 75, then C = 15

Charlie is 15 years old

4M = 3(15) + 3
4M = 48
M = 12

Megan is 12 years old

A - 12 = 8
A = 20

Anna is 20 years old