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.
