(a) Ali and Yusif shared N420.000.00 in the ratio 3.,; 5 : 8 respectively. Find the sum of Ali and Yusuf's shares (b) Solve: 2(\(\frac{1}{8}\))\(^x\) = 32\(...
Question 1 Report
(a) Ali and Yusif shared N420.000.00 in the ratio 3.,; 5 : 8 respectively. Find the sum of Ali and Yusuf's shares
(b) Solve: 2(\(\frac{1}{8}\))\(^x\) = 32\(^{x - 1}\).
Answer Details
(a) \(\text{N}420{,}000.00\) is shared in the ratio \(3:5:8\) (total \(16\) parts).
One part \(=\dfrac{420000}{16}=\text{N}26{,}250.00\).
Ali (3 parts) \(=\text{N}78{,}750\); Yusuf (5 parts) \(=\text{N}131{,}250\).
Sum of Ali and Yusuf's shares \(=(3+5)\times 26250=8\times 26250=\mathbf{\text{N}210{,}000.00}\).
(b) \(2\left(\dfrac{1}{8}\right)^{x}=32^{x-1}\).
Write in base 2: \(\dfrac{1}{8}=2^{-3},\ 32=2^{5}\).
\(2^{1}\cdot 2^{-3x}=2^{5(x-1)} \Rightarrow 2^{1-3x}=2^{5x-5}\).
\(1-3x=5x-5 \Rightarrow 6=8x \Rightarrow x=\dfrac{3}{4}\).
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