(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...
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 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 \(N300\):
\[300\left(1 + \tfrac{x}{100}\right)^2 - 300 = 6x + \tfrac{3}{4}\] \[300\left(\tfrac{2x}{100} + \tfrac{x^2}{10000}\right) = 6x + \tfrac{3}{4} \Rightarrow 6x + 0.03x^2 = 6x + 0.75\] \[0.03x^2 = 0.75 \Rightarrow x^2 = 25 \Rightarrow x = 5\]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 \(2 < x < 6\).
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