Answer: Since the alloy is made up of 93.5 parts aluminum, 5 parts zinc, and 1.5 parts copper, we can express the weight of zinc and copper needed to make the alloy as a ratio to the weight of aluminum needed. Let x be the weight of aluminum needed in pounds, then we have:
Weight of aluminum: Weight of zinc: Weight of copper = 93.5: 5 : 1.5
We know that the foundry has 164 pounds of aluminum available, so we can substitute x = 164 into the above ratio and solve for the weights of zinc and copper:
164: Weight of zinc: Weight of copper = 93.5: 5 : 1.5
Cross-multiplying, we get:
164 × 5 = 93.5 × Weight of zinc
Weight of zinc = (164 × 5) / 93.5
Weight of zinc = 8.76 pounds (rounded to two decimal places)
Similarly, cross-multiplying the above ratio gives us:
164: Weight of zinc: Weight of copper = 93.5: 5 : 1.5
164 × 1.5 = 93.5 × Weight of copper
Weight of copper = (164 × 1.5) / 93.5
Weight of copper = 2.63 pounds (rounded to two decimal places)
Therefore, the weight of zinc needed to make the alloy is 8.76 pounds and the weight of copper needed is 2.63 pounds.
Explanation: