Hello ben001.

The first question is: How much alloy contains 100 oz of fine gold, if the gold represents 58.3% of the alloy?

58.3% means \(\frac{58.3}{100}\) and that's 0.583

Let symbol x represent the ounces of alloy. Then 58.3% of x equals 100 and we can write:

0.583x = 100

To solve for x, we divide each side of that equation by 0.583

x = 100/0.583 and that's 171.5266

You can make about 171.53 ounces of 14k alloy using 100 ounces of fine gold.

To find the weights of the remaining metals, multiply the total ounces of alloy by the corresponding percents.

Copper: (0.23)(171.5266) = 39.4511

Nickel: (0.11)(171.5266) = 18.8679

Zinc: (0.077)(171.5266) = 13.2075

171.53 ounces of 14k gold alloy contains about

100 ounces of fine gold

39.45 ounces of copper

18.87 ounces of nickel

13.21 ounces of zinc

Cheers