(a) Lamin bought a book for N300.00 and sold it to... | WAEC SSCE - General Mathematics - 2018 (Essay)

Question 1 Report

(a) Lamin bought a book for N300.00 and sold it to Bola at a profit of x%. Bola then sold the same book at a profit of x%. If James paid \(N(6x + \frac{3}{4})\) more for the book than Lamin paid, find the value of x.

(b) Find the range of values of x which satisfies the inequality \(3x - 2 < 10 + x < 2 + 5x\).

Answer

(a) Lamin's cost is \(N300\). Selling to Bola at \(x\%\) profit means Bola pays \(300\left(1 + \frac{x}{100}\right)\).

Bola resells at another \(x\%\) profit, so James pays \(300\left(1 + \frac{x}{100}\right)^2\).

James pays \(N\left(6x + \frac{3}{4}\right)\) more than Lamin's \(N300\):

\[300\left(1 + \tfrac{x}{100}\right)^2 - 300 = 6x + \tfrac{3}{4}\] \[300\left(\tfrac{2x}{100} + \tfrac{x^2}{10000}\right) = 6x + \tfrac{3}{4} \Rightarrow 6x + 0.03x^2 = 6x + 0.75\] \[0.03x^2 = 0.75 \Rightarrow x^2 = 25 \Rightarrow x = 5\]

So \(x = 5\) (taking the positive value).

(b) Split \(3x - 2 < 10 + x < 2 + 5x\) into two inequalities.

Left: \(3x - 2 < 10 + x \Rightarrow 2x < 12 \Rightarrow x < 6\).

Right: \(10 + x < 2 + 5x \Rightarrow 8 < 4x \Rightarrow x > 2\).

Therefore \(2 < x < 6\).

Read lesson note on Variation (WAEC)

Read lesson note on Solution Of Linear Equations (WAEC)

Read lesson note on Inequalities (JAMB)

Answer Details

(a) Lamin's cost is \(N300\). Selling to Bola at \(x\%\) profit means Bola pays \(300\left(1 + \frac{x}{100}\right)\).

Bola resells at another \(x\%\) profit, so James pays \(300\left(1 + \frac{x}{100}\right)^2\).

James pays \(N\left(6x + \frac{3}{4}\right)\) more than Lamin's \(N300\):