x=# of ounces

30%x+90%(500)=40%(500+x)

0.3x+0.9(500)=0.4(500+x)

0.3x+450=200+0.4x

450-200=0.4x-0.3x

250=0.1x

2500=x

x=2500 ounces

Kelley J.

asked • 09/18/14I'm confused on how to even set this up to solve. Please help.

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x=# of ounces

30%x+90%(500)=40%(500+x)

0.3x+0.9(500)=0.4(500+x)

0.3x+450=200+0.4x

450-200=0.4x-0.3x

250=0.1x

2500=x

x=2500 ounces

Phillip R. answered • 09/19/14

Tutor

New to Wyzant
Top Notch Math and Science Tutoring from Brown Univ Grad

the final percentage is 40%

30% is 40 - 30 = 10% difference

90% is 90 - 40 = 50% difference

there we need 5 parts of the 30% alloy for every 1 part of the 90% alloy

We are told we are using 500 ounces of the 90% alloy.

Therefore we need 5 times that for the 30% alloy

5 x 500 = 2500 ounces

This is less complicated and much faster

Kristen B. answered • 09/19/14

Tutor

5.0
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BS in Chemistry / Strong Math Background

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 A_{30}, the alloy with 90% copper as A_{90}, and the alloy with 40% copper as A_{40}. We can set up an equation for the total amount of alloy as A_{30} + A_{90} = A_{40}. Since we know A_{90} = 500oz, A_{40} = A_{30}+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:

0.3A_{30} + 0.9A_{90} = 0.4A_{40}. We can substitute the know amount of A_{90} to get 0.3A_{30}+0.9(500)=0.4A_{40} or 0.3A30+450=0.4A_{40}

Now, if we combine the two equations, we can solve for A_{30}

0.3A_{30}+450=0.4(A_{30}+500), distribute the 0.4

0.3A_{30}+450=0.4A_{30}+200, subtract 200 and 0.3A_{30} from both sides

250=0.1A_{30 , }divide both sides by 0.1

A_{30}=2500oz

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.

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