Question 6
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A textbook company discovered that the profit made from selling its books is given by y = 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,
- form a quadratic equation in x;
- (using the quadratic formula, find, correct to the nearest whole number, the number of textbooks sold to make the profit.
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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 a tree is 28°. A bird perched at a point R, halfway up the tree.
- Represent the information in a diagram.
- Calculate, correct to the nearest degree, the angle of elevation of R from P.
Observation
The Chief Examiner reported that Candidates performance in this question was appreciable. However, they did better in part (a) than (b).
In part (a), they were expected to obtain 20,000 = x ^ 2 / 8 + 5x and thereafter multiply through by 8 and simplify to get x ^ 2 + 40x - 160,000=0.
Using the quadratic formula 
, where a = 1, b = 40 and c = – 160,000 
= 
= 
= 380.4997 or – 420. 4997
The number of books required to make the profit ≈ 380,500, correct to the nearest whole number.
In part (b), the required diagram is
From triangle PQR, tanX=(y/2)/w ⇒ y = 2w tan X-----------(1)
Also, from ∆ PTQ, tan 28°= y / w ⇒ y=w tan 28°-------(2)
Equating (1) and (2) yielded 2w tan X = w tan 28° so that
tanX =(w tan 28°)/ 2w = 0.5317 / 2 which implies that tan X = 0.2659
X = tan^(-1)(0.2659) = 15.42°.
The angle of elevation of R from P ≈ 15°, correct to the nearest degree.