Question

A metalworker has a metal alloy that is 20​% copper and another alloy that is 60​% copper. How many kilograms of each alloy should the metalworker combine to create 100 kg of a 52​% copper​ alloy?
The metalworker should use
_______ of the metal alloy that is 20​% copper and ___ kilograms
of the metal alloy that is 60​% copper
​(Type whole​ numbers.)

Answer 1

Answer:

• 20 kg of 20%
• 80 kg of 60%

Step-by-step explanation:

I like to use a little X diagram to work mixture problems like this. The constituent concentrations are on the left; the desired mix is in the middle, and the right legs of the X show the differences along the diagonal. These are the ratio numbers for the constituents. Reducing the ratio 32:8 gives 4:1, which totals 5 "ratio units". We need a total of 100 kg of alloy, so each "ratio unit" stands for 100 kg/5 = 20 kg of constituent.

That is, we need 80 kg of 60% alloy and 20 kg of 20% alloy for the product.

_____

Using an equation

If you want to write an equation for the amount of contributing alloy, it works best to let a variable represent the quantity of the highest-concentration contributor, the 60% alloy. Using x for the quantity of that (in kg), the amount of copper in the final alloy is ...

... 0.60x + 0.20(100 -x) = 0.52·100

... 0.40x = 32 . . . . . . . . . . .collect terms, subtract 20

... x = 32/0.40 = 80 . . . . . kg of 60% alloy

... (100 -80) = 20 . . . . . . . .kg of 20% alloy