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

Answer:

Olive's age = 32

Lisbeth's age = 8

Step-by-step 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