Hi Kelley. This problem does look confusing at first, but it's not as bad as it seems. It's best to start with what we know and set some variables. Let's set the total amount of the alloy with 30% copper as A30, the alloy with 90% copper as A90, and the alloy with 40% copper as A40. We can set up an equation for the total amount of alloy as A30 + A90 = A40. Since we know A90 = 500oz, A40 = A30+500
To solve this problem, we need to look at the actual amount of copper, not the alloys. We can set up an equation for the actual copper amounts like this:
0.3A30 + 0.9A90 = 0.4A40. We can substitute the know amount of A90 to get 0.3A30+0.9(500)=0.4A40 or 0.3A30+450=0.4A40
Now, if we combine the two equations, we can solve for A30
0.3A30+450=0.4(A30+500), distribute the 0.4
0.3A30+450=0.4A30+200, subtract 200 and 0.3A30 from both sides
250=0.1A30 , divide both sides by 0.1
We can check this answer with some quick math. 2500oz at 30% copper equals 750oz copper. 500oz at 90% copper equals 450oz copper. Total copper equals 1200oz copper (750+450=1200). The total amount of alloy is 2500oz + 500oz = 3000oz. If we divide the amount of copper by the total amount of alloy we get the % that is copper. 1200/3000=0.4 0r 40% copper.