In four years' time, Nana's mother will be three times as old as Nana. Six years ago, her mother was seven times as old as her. Find the following.

Question

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Answer 1

Let Nana's current age be x, and her mother's current age be y.

Step 1: Translate into equations

“In four years, Nana’s mother will be three times as old as Nana” which means

y + 4 = 3 * (x + 4)

y + 4 = 3x + 12

y - 3x = 8 so this is Equation 1

“Six years ago, her mother was seven times as old as Nana”

y - 6 = 7 * (x - 6)

y - 6 = 7x - 42

y - 7x = -36 so this is Equation 2

Step 2: Solve the system of equations

Equations:

1) y - 3x = 8

2) y - 7x = -36

Subtract Equation 2 from Equation 1

(y - 3x) - (y - 7x) = 8 - (-36)

y - 3x - y + 7x = 44

4x = 44

x = 11

Plug x = 11 into any of the equation let's take Equation 1

y - 3*11 = 8

y - 33 = 8

y = 41

Hence,

Nana’s age = 11 years

Mother’s age = 41 years