(a) A radio which a dealer bought for N6,000.00 and marked to give a profit of 30% was reduced in a sales by 10%. Find : (i) the final sales price ; (ii) the percentage profit.
(b) Solve the equation : \(2^{(2x + 1)} - 9(2^{x}) + 4 = 0\).
Show Answer Show Explanation Explanation (a) Cost price of a radio = N6,000.00 \(\therefore\) 30% profit = \(\N6000 \times \frac{30}{100} = N1800\) \(\therefore\) Marked price = N(6000 + 1800) = N7800 Final Selling price = \(\frac{100 - 10}{100} \times N7800 = N7020\) Profit = N(7020 - 6000) = N1020. \(\therefore\) % profit = \(\frac{1020}{6000} \times 100% = 17%\) (b) \(2^{(2x + 1)} - 9(2^{x}) + 4 = 0\) \((2^{x})^{2} \times 2 - 9(2^{x}) + 4 = 0\) Let \(2^{x} = y\) \(2y^{2} - 9y + 4 = 0\) \(2y^{2} - 8y - y + 4 = 0\) \(2y(y - 4) - 1(y - 4) = 0\) \((2y - 1)(y - 4) = 0\) \(2y = 1 \implies y = \frac{1}{2}; y = 4\) \(y = \frac{1}{2} \implies 2^{x} = \frac{1}{2} = 2^{-1} \) \(x = -1\) \(y = 4 \implies 2^{x} = 4 = 2^{2}\) \(x = 2\) \(\therefore x = -1, 2\)