Question 164971
An alloy of metals is 25% copper.  Another alloy is 50% copper.  how much of each alloy should be used to make 1000 grams of an alloy that is 45% copper?

We have a system of equation in two variables.

Let x = alloy of metal

Let y = Another alloy

THEN:

x + y = 1000...Equation A

The question tells us that 25% is copper and that the other alloy is 50% copper.

From this information we make our second equation.

0.25x + 0.50x = 0.45 (1000)...Equation B

Here is your system of equations:

x + y = 1000...Equation A

0.25x + 0.50y = 0.45 (1000)...Equation B

I will solve for y in Equation A. Of course, you can solve for x or y (your choice).

From this system of equations, it is easier playing with equation A.

x + y = 1000...Equation A

Solving for x, I get:

x = 1000 - y

I will now plug x = 1000 - y into Equation B to find the value of y.

0.25x + 0.50y = 0.45 times (1000)

0.25(1000 - y) + 0.50y = 450

250 - 0.25y + 0.50y = 450

250 + 0.25y = 450

0.25y = 450 - 250

0.25y = 200

y = 200/0.25

y = 800

We just found the value of y to be 800.

To find x, we plug y = 800 for y in EITHER Equation A or Equation B.

I will select the easy Equation A.

x + y = 1000...Equation A

x + 800 = 1000

Solving for x, I get:

x = 1000 - 800

x = 200

Finals answer:  200 alloy of metal should be used and 800 of the other alloy should be used.