x - the mass of the first alloy (15%)
y - the mass of the second alloy (75%)
x kg of the first alloy contains 15%x=0.15x=(15/100)x=(3/20)x kg of copper
y kg of the second alloy contains 75%y=0.75y=(75/100)y=(3/4)y kg of copper
90 kg of a 51% copper alloy contains 51%*90=0.51*90=45.9 kg of copper
[tex]x+y=90 \\
\frac{3}{20}x+\frac{3}{4}y=45.9 \ \ \ |\times (-\frac{4}{3}) \\ \\
x+y=90 \\
\underline{-\frac{1}{5}x-y=-61.2} \\
x-\frac{1}{5}x=90-61.2 \\
\frac{4}{5}x=28.8 \ \ \ |\times \frac{5}{4} \\
x=36 \\ \\
36+y=90 \\
y=90-36 \\
y=54[/tex]
The metal worker should combine 36 kg of the 15% copper alloy and 54 kg of the 75% copper alloy to create 90 kilograms of a 51% copper alloy.
