Answer:
- x +y = 500
- 0.65x +0.95y = 0.75(500)
- solution: (x, y) = (300, 200)
Step-by-step explanation:
A system of equations for the problem can be written using the two given relationships between quantities of brass alloys.
<h3>Setup</h3>
Let x and y represent the quantities in grams of the 65% and 90% alloys used, respectively. There are two relations given in the problem statement.
x + y = 500 . . . . . . quantity of new alloy needed
0.65x +0.90y = 0.75(500) . . . . . quantity of copper in the new alloy
These are the desired system of equations.
<h3>Solution</h3>
This problem does not ask for the solution, but it is easily found using substitution for x.
x = 500 -y
0.65(500 -y) +0.90y = 0.75(500)
(0.90 -0.65)y = 500(0.75 -0.65) . . . . . . subtract 0.65(500)
y = 500(0.10/0.25) = 200
x = 500 -200 = 300
300 grams of 65% copper and 200 grams of 90% copper are needed.
