WAEC 2016 · Paper 2 · Q1

(a)
Simplify: $\dfrac{6\frac14 - 3\frac25}{2\frac12 - 1\frac35}$ .
(b)
The average age of students in a class is 15 years. When the teacher's age of 45 years is added, the average age becomes 18. How many students are in the class?

Worked solution (try it first)

(a)

Work out the top and the bottom separately.
Top: $6\frac14 - 3\frac25 = \frac{25}{4} - \frac{17}{5}$
$= \frac{125 - 68}{20}$
$= \frac{57}{20}$ .
Bottom: $2\frac12 - 1\frac35 = \frac52 - \frac85$
$= \frac{25 - 16}{10}$
$= \frac{9}{10}$ .
Then divide: $\frac{57}{20} \div \frac{9}{10} = \frac{57}{20} \times \frac{10}{9}$
$= \frac{570}{180}$
$= \frac{19}{6}$
$= 3\frac16$ .

(b)

Let there be $n$ students.
Their ages add up to $15n$ (mean × number).
Adding the teacher makes $n + 1$ people with a total age of $15n + 45$ and a mean of 18: $\frac{15n + 45}{n + 1} = 18$ .
So $15n + 45 = 18n + 18$ , which gives $3n = 27$ and $n = 9$ .
There are 9 students.
Check: 9 students total 135 years.
With the teacher, $\frac{180}{10} = 18$ .

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