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A manufacturer creates an alloy using only copper and tin. What percentage of the alloy is copper by weight?
(1) If the weight of the tin is increased by 50%, the total weight of the alloy becomes 9 kilograms.
(2) If the weight of the tin is increased by 200%, the total weight of the alloy increases by 50%.
(1) If the weight of the tin is increased by 50%, the total weight of the alloy becomes 9 kilograms.
(2) If the weight of the tin is increased by 200%, the total weight of the alloy increases by 50%.
08 Jan 2025, 05:05
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Official Solution:
A manufacturer creates an alloy using only copper and tin. What percentage of the alloy is copper by weight?
Assuming the weight of copper is \(c\) and the weight of tin is \(t\), we need to find the value of \(\frac{c}{c + t} * 100\).
(1) If the weight of the tin is increased by 50%, the total weight of the alloy becomes 9 kilograms.
This implies \(c + 1.5t = 9\). Without additional information, the exact values of \(c\) and \(t\), or their ratio, cannot be determined. Not sufficient.
(2) If the weight of the tin is increased by 200%, the total weight of the alloy increases by 50%.
This implies \(c + 3t = 1.5(c + t)\), which simplifies to \(c = 3t\). Substituting into\(\frac{c}{c + t} * 100\) gives \(\frac{3t}{3t + t} * 100=75\%\). Sufficient.
Answer: B
A manufacturer creates an alloy using only copper and tin. What percentage of the alloy is copper by weight?
Assuming the weight of copper is \(c\) and the weight of tin is \(t\), we need to find the value of \(\frac{c}{c + t} * 100\).
(1) If the weight of the tin is increased by 50%, the total weight of the alloy becomes 9 kilograms.
This implies \(c + 1.5t = 9\). Without additional information, the exact values of \(c\) and \(t\), or their ratio, cannot be determined. Not sufficient.
(2) If the weight of the tin is increased by 200%, the total weight of the alloy increases by 50%.
This implies \(c + 3t = 1.5(c + t)\), which simplifies to \(c = 3t\). Substituting into\(\frac{c}{c + t} * 100\) gives \(\frac{3t}{3t + t} * 100=75\%\). Sufficient.
Answer: B
