Let x pounds of 30% copper alloy should be added to 25 pounds of a second alloy that is 20% copper to create y pounds of a 27% alloy.
Therefore, we can frame two equations as:
[tex]x+25=y[/tex]
[tex]0.30x+0.20*25=0.27y[/tex]
Our next step is to solve this system of linear equations. We can use substitution method to solve this system.
[tex]0.30x+0.20*25=0.27(x+25)\\ 0.30x+5=0.27x+6.75\\ 0.03x=1.75\\ x=\frac{1.75}{0.03} \\ x=58.33 \text{ pounds}[/tex]
Therefore, 58.33 pounds of 30% copper alloy must be added.
