SOLUTION: A chemist has two alloys, one of which is 15% gold and 25% lead and the other which is 40% gold and 30% lead. How many grams of each of the two alloys should be used to make an all

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Question 707567: A chemist has two alloys, one of which is 15% gold and 25% lead and the other which is 40% gold and 30% lead. How many grams of each of the two alloys should be used to make an alloy that contains 76.5 g of gold and 116.5 g of lead?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Allow 1, x
Allow 2, y

Accounting for the quantity of gold: 0.15x+0.40y=76.5 grams of Gold. Note this uses both alloys available, as does the next equation;

Account for the quantity of lead: 0.25x+0.30y=116.5 grams Lead.

System to start with is this:
0.15x%2B0.40y=76.5
0.25x%2B0.30y=116.5

This will help to eliminate terms of y and to first solve for x.
3*(0.15x%2B0.40y=76.5)
4*(0.25x%2B0.30y=116.5)
Subtract one equation from the other.

....and THIS may help to eliminate terms of x and solve for y.
5*(0.15x%2B0.40y=76.5)
3*(0.25x%2B0.30y=116.5)
Subtract one equation from the other.