Question

A metalworker has a metal alloy that is 15% copper and another alloy that is 65% copper. How many kilograms of each alloy should the metalworker combine to create 60 kg of a 55% copper alloy?

Answer 1

Iggy, this is the solution:

First metall alloy = 15% Copper

Second metal alloy = 65% Copper

60 kg of the mix = 60 * 0.55 Copper = 33 kilograms of copper

Let x to represent the number of kilograms of the first alloy

Let y to represent the number of kilograms of the second alloy

x + y = 60

x = 60 - y

For solving for y, we have:

0.15x + 0.65y = 60 * 0.55

0.15 (60 - y) + 0.65y = 33

9 - 0.15y + 0.65y = 33

9 + 0.5y = 33

Subtracting 9 at both sides:

9 + 0.5y - 9 = 33 - 9

0.5y = 24

Multiplying by 2 at both sides:

0.5y * 2 = 24 * 2

y = 48 (The metalworker needs 48 kilograms of the second alloy)

For solving for x, we have:

x + y = 60

x + 48 = 60

x = 60 - 48

x = 12 (The metalworker needs 12 kilograms of the first alloy)