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A metalworker has a metal alloy that is 15% copper and another alloy that is 75% copper. How many kilograms of each alloy should the metal worker combine to create 90 kilograms of a 51% copper alloy?

Sagot :

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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.
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