Question

A metal alloy is a metal made by blending 2 or more types of metal. A jeweler has supplies of two metal alloys. One alloy is 30% gold and the other is 10% gold. How much of each alloy should the jeweler combine to create 4 kg of an alloy containing 15% gold?

Answer 1

1 kg of 30% gold and 3 kg of 10% gold

Explanation:

Let us take "x" kg of 30% gold, and

"y" kg of 10% gold

We need to make 4 kg of 15% gold, that would be:

4(15%) = 4 (15/100) = 4(0.15) = 0.6kg

We can now write an equation as:

30%x + 10%y = 4(0.15)

0.3x + 0.1y = 0.6 (equation 1)

Also, we know there will be 4 kg from "x" and "y", so we can write:

x + y = 4

or x = 4 - y

We substitute this into equation 1 and solve for y first:

0.3x + 0.1y = 0.6

0.3(4 - y) + 0.1y = 0.6

1.2 - 0.3y + 0.1y = 0.6

0.2y = 0.6

y = 3

And x = 4 - y, x = 4 - 3 = 1

So,

1 kg of 30% gold and 3 kg of 10% gold