Question

A metal worker has a metal alloy that is 20% copper and another alloy that is 65% copper. How many kilograms of each alloy should the metalworker combine to create 90 kg of a 56% copper alloy?

Answer 1

To create 90 kg of a 56% copper alloy, the metalworker should combine 18 kg of the 20% copper alloy and 72 kg of the 65% copper alloy.

Step-by-step explanation:

The question involves creating a 56% copper alloy from two existing alloys with different copper contents. To solve this, we use a system of equations to find the mass of each alloy needed. Let x be the kilograms of the 20% copper alloy and y be the kilograms of the 65% copper alloy. The sum of the two alloys should be 90 kg:

• x + y = 90

The total amount of copper in the resulting alloy should be 56% of 90 kg:

• 0.20x + 0.65y = 0.56 × 90

Now we solve the system of equations. The first equation gives us y = 90 - x. Substituting y into the second equation we get:

• 0.20x + 0.65(90 - x) = 50.4

Simplifying and solving for x, we find:

• 0.20x + 58.5 - 0.65x = 50.4
• -0.45x = -8.1
• x = 18

So the metalworker needs 18 kg of the 20% copper alloy. Using the first equation, we find y = 90 - 18 = 72 kg for the 65% copper alloy.

The metalworker should combine 18 kg of the 20% copper alloy and 72 kg of the 65% copper alloy to create a 56% copper alloy that totals 90 kg.