WAEC 2018 · Paper 2 · Q2

Linear & simultaneous equations

(a)
Musa is three years older than Manya. Seven years ago, Musa was twice as old as Manya. How old are they now?
Separate values with commas, e.g. 3, −2
(b)
In how many years will the sum of their ages be 45?

Worked solution (try it first)

(a)

Let Manya's age now be $x$ years.
Musa is three years older: $x + 3$ years.
Seven years ago they were $x - 7$ and $x + 3 - 7 = x - 4$ .
Musa was twice as old as Manya: $x - 4 = 2(x - 7)$ .
Expand: $x - 4 = 2x - 14$ .
So $x = 10$ .
Manya is 10 years old and Musa is 13.
Check: seven years ago they were 3 and 6, and 6 is twice 3 ✓.

(b)

In $n$ years they will be $10 + n$ and $13 + n$ .
Their sum is 45: $(10 + n) + (13 + n) = 45$ .
So $23 + 2n = 45$ , $2n = 22$ and $n = 11$ .
In 11 years.

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