(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 \(3x - 2 < 10 + x < 2 + 5x\).
Explanation
(a) S.P = \(C.P + \frac{% profit}{100} \times C.P\) = \(300 + (\frac{x}{100} \times 300)\) S.P = N(300 + 3x) Therefore, Bola bought it at N(300 + 3x). James paid \(N(6x + \frac{3}{4})\) extra from what Lamin paid, therefore Bola's S.P = \(N(300 + 6x + \frac{3}{4})\) = N(300.75 + 6x). Profit for Bola = \(N(300.75 + 6x - (300 + 3x)) = N(0.75 + 3x)\) \(\frac{x}{100} \times N(300 + 3x) = N(0.75 + 3x)\) \(300x + 3x^{2} = 75 + 300x\) \(\implies 3x^{2} = 75\) \(x^{2} = 25 \therefore x = 5\) (b) \(3x - 2 < 10 + x < 2 + 5x\) \(3x - 2 < 10 + x \implies 3x - x < 10 + 2\) \(2x < 12 \implies x < 6\) \(10 + x < 2 + 5x\) \(x - 5x < 2 - 10\) \(-4x < -8 \implies x > 2\) The range = \(2 < x < 6\)