Question

George and Paul use a metal alloy that is 18.1% copper to make jewelry. How many ounces of an alloy that is 14% copper must be mixed with an alloy that is 23% copper to form 90 ounces of the desired alloy?

Answer 1

Use 49 ounces of the 14% allow and 41 ounces of the 23% alloy.

Explanation:

Each ounce of the 14% copper contains 0.14 ounce of pure copper.

Each ounce of the 23% copper contains 0.23 ounce of pure copper.

Each ounce of the 18.1% copper contains 0.181 ounce of pure copper.

Use x ounces of the 14% and y ounces of the 23% to make 90 ounces of 18.1% alloy.

x+y = 90

y = 90-x

0.14x + 0.23y = 0.181·90

0.14x + 0.23(90-x) = 16.29

0.14x + 20.7 - 0.23x = 16.29

-0.09x + 20.7 = 16.29

4.41 = 0.09x

x = 49

y = 90-x = 41

Use 49 ounces of the 14% allow and 41 ounces of the 23% alloy.