Question

A metalworker has a metal alloy that is 25% copper and another alloy that is 70%. How many kilograms of each alloy should the metalworker combine to create 50kg of a 61% copper alloy?

Answer 1

I believe this question requires you to set up a system of equations.

Let x = the total mass (in kg) of the 25% copper alloy

Let x = the total mass (in kg) of the 70% copper alloy

Thus, you can form two equations with the data provided:

0.7(y) + 0.25(x) = 0.61(50)

y + x = 50

Using "y+x=50"

x = 50 - y

Plus "x = 50-y" into the other equation. Note that 0.61(50) = 30.5

0.7y + 0.25(50-y) = 30.5

Distribute 0.25 over (50-y)

0.7y + 12.5 - 0.25y = 30.5

Subtract 12.5 from both sides and add 0.7y to -0.25y

0.45y = 18

Dividing 0.45 on each side leaves you with y = 40

Now, plug y = 40 in "x + y = 50" to solve for the total mass of the 25% copper alloy.

x + 40 = 50

x = 10

Thus, you need 10 kilograms of the 25% alloy combined with 40 kilograms of the 70% alloy to create a 50 kilogram alloy composed of 61% copper.

Hope this helps!