Question

Two years ago, Lisbeth's age was a fifth of Olivia's age. In four years, Olivia's age will be three times Lisbeth's age. How old are they now?

Answer 1

Olive's age = 32

Lisbeth's age = 8

Explanation:

Declaration

Let Eisbeths present age = x

Let Olive's age = y

Equations

(x - 2) = 1/5 (y - 2)

x + 4 = 1/3(Y + 4)

Solution

1st equation

(x - 2) = 1/5 (y - 2) Multiply both sides by 5

5(x - 2) = y - 2 Remove the brackets

5x - 10 = y - 2 Add 10 to both sides

5x -10+10 = y - 2+10 Combine

5x = y + 8 Subtract 8 from both sides

5x - 8 = y + 8 - 8 Combine

5x - 8 = y

2nd Equation

x + 4 = 1/3(y + 4) Multiply both sides by 3

3(x + 4) = y + 4 Remove the brackets

3x + 12 = y + 4 Subtract 3 from both sides

3x + 12 - 4 = y + 4 - 4 Combine

3x + 8 = y

Note Since y is the same in both equations, the left side of each can be thought of as equal to each other.

3x + 8 = 5x - 8 Add 8 to both sides

3x + 8 + 8 = 5x - 8 + 8 Combine

3x + 16 = 5x Subtract 3x from both sides

3x - 3x + 16 = 5x - 3x Combine

16 = 2x Divide by 2

16/2 = 2x/2

8 = x

y = 3x + 8

y = 32