Question

A metallurgist has one alloy containing26 % copper and another containing69 % copper. How many pounds of each alloy must he use to make53 pounds of a third alloy containing50 % copper? (Round to two decimal places if necessary.)

Answer 1

23.42 pounds of the alloy with 26% copper

29.58 pounds of the alloy with 69% copper

Step-by-step explanation:

Let's call X the number of pounds of the alloy with 26% copper and Y the number of pounds of the alloy with 69% copper.

We need 53 pounds of the third alloy, so we can write the following equation:

X + Y = 53

Additionally, the third alloy should be 50% copper. So, the second equation is:

0.26X + 0.69Y = 0.5(53)

0.26X + 0.69Y = 26.5

Now, we can solve for X in the first equation and replace it on the second:

`\begin{gathered} X+Y=53 \\ X=53-Y \end{gathered}`
`\begin{gathered} 0.26X+0.69Y=26.5 \\ 0.26(53-Y)+0.69Y=26.5 \end{gathered}`

So, solving for Y, we get:

`\begin{gathered} 0.26\cdot53-0.26Y+0.69Y=26.5 \\ 13.78+0.43Y=26.5 \\ 0.43Y=26.5-13.78 \\ 0.43Y=12.72 \\ Y=(12.72)/(0.43) \\ Y=29.58 \end{gathered}`

Then, the value of X is:

`\begin{gathered} X=53-Y \\ X=53-29.58 \\ X=23.42 \end{gathered}`

Therefore, you need to use 23.42 pounds of the alloy with 26% copper and 29.58 pounds of the alloy with 69% copper