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

Algebra.Com
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)   (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:



This will help to eliminate terms of y and to first solve for x.
3*()
4*()
Subtract one equation from the other.

....and THIS may help to eliminate terms of x and solve for y.
5*()
3*()
Subtract one equation from the other.
RELATED QUESTIONS

A chemist has two alloys, one of which is 15% gold and 15% lead and the other which is... (answered by josgarithmetic)
A chemist has two alloys, one of which is 5% gold and 25% lead and the other which is 40% (answered by ikleyn)
A chemist has two alloys, one of which is 15% gold and 25% lead and the other which is... (answered by ankor@dixie-net.com)
Chemistry: a chemist has two alloys, one of which is 10% gold and 15% lead, and the other (answered by gonzo)
A chemist has two alloys, one of which is 10% gold and 15% lead, and the other of which... (answered by arallie)
A chemist has two alloys, one of which is 15% gold and 20% lead and the other which is... (answered by ikleyn)
A chemist has two alloys, one of which is 10% gold and 25% lead and the other which is... (answered by josgarithmetic)
A chemist has two alloys, one of which is 5% gold and 10% lead and the other which is 30% (answered by josgarithmetic)
A chemist has two alloys, one of which is 5% gold and 15% lead and the other which is 20% (answered by ankor@dixie-net.com)