WAEC 2010 · Paper 2 · Q2

(a)
(i) Solve the inequality $\frac12x - \frac56(x + 2) \le 1 + x$ . (ii) Illustrate the solution on a number line.
Model answer
A solid dot at $-2$ (it is included) with an arrow to the right.
(b)
When the price of an apple increased by ₦5.00, 18 apples cost ₦60.00 more than 20 apples cost before the increase. Find the new price of an apple.

Worked solution (try it first)

(a)(i)

Multiply every term by 6 (the LCM of 2 and 6): $3x - 5(x + 2) \le 6 + 6x$ .
Expand the bracket: $3x - 5x - 10 \le 6 + 6x$ , so $-2x - 10 \le 6 + 6x$ .
Collect terms: $-8x \le 16$ .
Divide by $-8$ and reverse the sign: $x \ge -2$ .

(ii)

On the number line, put a solid dot at $-2$ (because $-2$ is included) and draw an arrow from it to the right.

(b)

Let the old price be ₦ $x$ .
The new price is ₦ $(x + 5)$ .
18 apples at the new price cost ₦60 more than 20 at the old price: $18(x + 5) - 20x = 60$ .
Expand: $18x + 90 - 20x = 60$ , so $-2x = -30$ and $x = 15$ .
The new price is $15 + 5 =$ ₦20.00.

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