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
