WAEC 2023 · Paper 2 · Q7

(a)
Aman spent $\frac13$ of his income on rent, $\frac16$ of the income in a fast food shop and $\frac34$ of the remaining amount was saved in a bank. If he had ₦125,000.00 left, find: (i) his income; (ii) the amount saved in the bank.
Separate values with commas, e.g. 3, −2
(b)
Solve: $\dfrac{2 + 3x}{5} - \dfrac{1 - 7x}{3} < 2x + 9$ .
Show the answer
$x < \frac{67}{7}$

Worked solution (try it first)

(a)

Rent and food take $\frac13 + \frac16 = \frac12$ of his income, leaving $\frac12$ .
He saves $\frac34$ of that: $\frac34 \times \frac12 = \frac38$ .
What's left is $\frac12 - \frac38 = \frac18$ of his income.

(i)

$\frac18$ of his income is ₦125,000, so his income is $8 \times 125\,000 = ₦1,000,000$ .

(ii)

Saved: $\frac38 \times 1\,000\,000 = ₦375,000$ .

(b)

Multiply every term by 15 (the LCM of 5 and 3): $3(2 + 3x) - 5(1 - 7x) < 15(2x + 9)$ , so $6 + 9x - 5 + 35x < 30x + 135$ .
Then $44x + 1 < 30x + 135$ , so $14x < 134$ and $x < \frac{67}{7}$ (that is, $x < 9\frac47$ ).

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