Ametallurgist has one alloy containing 26%26% copper and another containing 69%69% copper. how many pounds of each alloy must he use to make 5353 pounds of a third alloy containing 50%50% copper? (round to two decimal places if necessary.)

Ans. He must use 2,987.76 pounds of alloy X (Cu=69%) and 2,365.24 pounds of alloy Y (26%=Cu)

Explanation:

Hi, let´s call alloy X the alloy that contains 69% of Cu and alloy Y the one containing 26% of Cu. Since he needs to produce 5,353 pounds of alloy, the first equation that we need to use is the following.

Now, we need this 5,353 pounds of the new alloy to be 50% Cu, therefore, we have to use a portion of alloy X and alloy Y. This is as follows.

And we have already established that X+Y is equal to 5,353, therefore this equation should look like this.

And we solve for X this equation, this as follows.

Now, we use this result and substitute this for X in the first equation like this.

and then, we solve for Y

So, he needs to use 2,365.24 pounds of alloy that contains 26% of Cu, this means that the rest (2,987.76 pounds) must come from the alloy that contains 69% of Cu.

We can check this result by finding the overall Cu obtained by this amounts of alloy, that is

That adds up to 2,676.51 pounds of pure Cu, and since the total weight of the new alloy is 5,353, this amount of copper makes up for:

50% of the total weight.

Best of luck.

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