math 171 question 3

Question

To form a new conductor, a metallurgist must mix an alloy with that has 75% gold content and an alloy that has 98% gold content to obtain 32 ounces of a new alloy that has 80% gold content. How many ounces of each of the original alloys must be used?

Answer 1

Let A represent the ounces of the first alloy.

Let B represent the ounces of the second alloy.

Create a system of equations.

First, for the total desired weight:

A + B = 32

Then for the desired gold concentration:

0.75A + 0.98B = 0.8*32

Solving this system of equations gives us approximately.

A = 25.043, B = 6.957

Check your answer:

25.043 + 6.957 = 32

0.75*25.043 + 0.98*6.957 = 25.6, which is 80% of 32