(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) th...
Question 1 Report
(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 : \(2^{(2x + 1)} - 9(2^{x}) + 4 = 0\).
Answer Details
(a)(i) Final sales price. Marked price for a 30% profit:
\[\text{MP} = 6000\times1.30 = \text{N}7800.\]
Reduced by 10% in the sales:
\[\text{Sales price} = 7800\times0.90 = \text{N}7020.\]
(a)(ii) Percentage profit.
\[\%\text{ profit} = \frac{7020 - 6000}{6000}\times100 = \frac{1020}{6000}\times100 = 17\%.\]
(b) Let \(u = 2^x\). Then \(2^{(2x+1)} = 2\cdot2^{2x} = 2u^2\), so the equation becomes
\[2u^2 - 9u + 4 = 0 \Rightarrow (2u - 1)(u - 4) = 0.\]
\[u = 4\ \Rightarrow\ 2^x = 4\ \Rightarrow\ x = 2;\qquad u = \tfrac{1}{2}\ \Rightarrow\ 2^x = 2^{-1}\ \Rightarrow\ x = -1.\]
Answer: \(x = 2\) or \(x = -1\).
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