(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).
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)