If [tex]a[/tex] is the amount (by weight) of the first alloy that you will use, then the new alloy will have a total weight of [tex]25+a[/tex].
The second alloy has 5 pounds of copper (20% of 25 = 5). 30% of the first alloy is copper, so that the amount of copper being introduced is [tex]0.30a[/tex], making the total amount of copper in the new alloy [tex]5+0.30a[/tex].
We want the proportion of copper in the new alloy to come out to 27% of the new alloy's weight, so that
[tex]\dfrac{5+0.30a}{25+a}=0.27\implies a=\dfrac{175}3\approx58.3[/tex]
