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HALP, plz explain steps,
A metal alloy is a mixture of two or more metals. A jeweler wants to make 8 grams of 18-carat gold, which is 75% gold. The jeweler has an alloy that is 90% gold and an alloy that is 50% gold. How much of each alloy does he use?

please use a system of equations to explain, would help, and maybe use elimination



Answer :

Hippalectryon
Let's say he's gonna use x grams of 90% gold alloy and y grams of 50% gold alloy.

The total percentage of gold in the mixture will thus be (x*0.9+y*0.5)/8=0.75 (=75%)

What is more x+y=8

The system is thus x+y=8, 0.9x+0.5y=8*0.75=6
From the first one we get y=8-x, which we insert in the second one : x(0.9-0.5)+0.5*8=4 hence x=(6-0.5*8)/(0.4)=5 and y=8-5=3

The answer is 5 grams of 90% gold and 3 grams of 50% gold

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