Question

Brass is an alloy made by melting and mixing copper and zinc. A metallurgist has two brass

alloys, one that is 65% copper and one that is 90% copper. He would like to combine a
portion of each alloy to produce 500 g of a new alloy that is 75% copper.

Write a system of equations for this problem

Answer 1

• x +y = 500
• 0.65x +0.95y = 0.75(500)
• solution: (x, y) = (300, 200)

Explanation:

A system of equations for the problem can be written using the two given relationships between quantities of brass alloys.

Setup

Let x and y represent the quantities in grams of the 65% and 90% alloys used, respectively. There are two relations given in the problem statement.

x + y = 500 . . . . . . quantity of new alloy needed

0.65x +0.90y = 0.75(500) . . . . . quantity of copper in the new alloy

These are the desired system of equations.

Solution

This problem does not ask for the solution, but it is easily found using substitution for x.

x = 500 -y

0.65(500 -y) +0.90y = 0.75(500)

(0.90 -0.65)y = 500(0.75 -0.65) . . . . . . subtract 0.65(500)

y = 500(0.10/0.25) = 200

x = 500 -200 = 300

300 grams of 65% copper and 200 grams of 90% copper are needed.