Question

A metalworker has a metal alloy that is 20​% copper and another alloy that is 70​% copper. How many kilograms of each alloy should the metalworker combine to create 90 kg of a 50​% copper​ alloy?

Answer 1

Answer: combine 36 kg 20% copper alloy and 54 kg 70% copper alloy.

Explanation

Construct your system of equations:

1) Variables:

x = kg of alloy with 20% copper content
y = kg of alloy with 70% copper content

2) First equation:

90 kg of alloy => 90  = x + y

3) Second equation:

90 kg 50% copper = 90 kg * 0.5 = 45 kg copper

x kg 20% copper = 0.2x

y kg 70% copper = 0.7y

=> 45 = 0.2x + 0.7y

4) System

x + y = 90
0.2x + 0.7y = 45

Solve the system

5) Mutiply the first equation times 0.2:

0.2x + 0.2y = 18

6) Subtract from the second equation:

0.2x - 0.2x + 0.7y - 0.2y = 45 - 18

0.5y = 27

y = 27 / 0.5 = 54

7) Replace into the first equation fo find x:

x = 90 - 54 = 36

Answer: 36 kg 20% copper alloy and 54 kg 70% copper alloy.