Two alloys A and B contain copper and zinc in the ratio \(3:4\) and \(5:9\), respectively. If equal weights of both alloys are melted together to form a new alloy, what is the ratio of copper to zinc in the new alloy?
11:17
Alloy A has copper and zinc in the ratio \(3:4\), so 7 parts total.
Alloy B has copper and zinc in the ratio \(5:9\), so 14 parts total.
To take equal weights, use 14 units of each alloy (a common multiple of 7 and 14).
In 14 units of A: copper \(= \frac{3}{7} \times 14 = 6\) and zinc \(= \frac{4}{7} \times 14 = 8\).
In 14 units of B: copper \(= \frac{5}{14} \times 14 = 5\) and zinc \(= \frac{9}{14} \times 14 = 9\).
Total copper \(= 6 + 5 = 11\) and total zinc \(= 8 + 9 = 17\).
Hence, the ratio of copper to zinc in the new alloy is 11:17.
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