(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)