WAEC 2018 · Paper 2 · Q6

(a)
A textbook company discovered that the profit made from selling its books is given by $y = \dfrac{x^2}{8} + 5x$ , where $x$ is the number of textbooks sold (in thousands) and $y$ is the corresponding profit (in Ghana cedis). If the company made a profit of GH₵ 20,000.00, (i) form a quadratic equation in $x$ ; (ii) using the quadratic formula, find the number of textbooks sold to make the profit.
(b)
The angle of elevation of the top $T$ of a tree from a point $P$ on the same ground level as the foot $Q$ of the tree is $28^\circ$ . A bird perched at a point $R$ , halfway up the tree. (i) Represent the information in a diagram. (ii) Calculate, correct to the nearest degree, the angle of elevation of $R$ from $P$ .

Worked solution (try it first)

Formula with $a = 1$ , $b = 40$ , $c = -160\,000$ : $x = \frac{-40 \pm \sqrt{40^2 + 4 \times 160\,000}}{2}$
$= \frac{-40 \pm \sqrt{641\,600}}{2}$
$= \frac{-40 \pm 801.0}{2}$ .
The number sold can't be negative, so $x \approx 380.5$ (thousand): about 380,500 books.

Let $|PQ| = d$ .
Then $|QT| = d\tan 28^\circ$ , and $|QR| = \frac12 d\tan 28^\circ$ .
So $\tan\angle QPR = \frac{|QR|}{d}$
$= \frac12\tan 28^\circ$
$\approx 0.2659$ , and the angle of elevation of $R$ is about $14.9^\circ \approx 15^\circ$ .