To solve this problem, we need to set up a system of equations.
Let's represent the amount of the 20% alloy as x (in ounces). Since we want a total of 100 ounces of the desired alloy, the amount of the 27% alloy would be 100 - x.
Now, we need to set up the equation based on the copper content.
The amount of copper in the 20% alloy is 0.20x ounces.
The amount of copper in the 27% alloy is 0.27(100 - x) ounces.
The total amount of copper in the final alloy is 24.9% of 100 ounces, which is 0.249(100) ounces.
Setting up the equation:
0.20x + 0.27(100 - x) = 0.249(100)
Now we can solve for x:
0.20x + 27 - 0.27x = 24.9
0.20x - 0.27x = 24.9 - 27
-0.07x = -2.1
x = -2.1 / (-0.07)
x = 30
Therefore, 30 ounces of the 20% alloy should be mixed with 70 ounces of the 27% alloy to form 100 ounces of the desired alloy.