SOLUTION: A chemist has two alloys, one of which is 5% gold and 10% lead and the other which is 30% gold and 40% lead. How many grams of each of the two alloys should be used to make an allo

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Question 713067: A chemist has two alloys, one of which is 5% gold and 10% lead and the other which is 30% gold and 40% lead. How many grams of each of the two alloys should be used to make an alloy that contains 39 g of gold and 68 g of lead?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Variables to use:
u grams of the low concentrated alloy
v grams of the high concentrated alloy

The low concentration alloy, alloy L, is 5% gold and 10% lead. High concentration alloy, alloy H, is 30% gold and 40% lead.

System to solve
u%2A5%2Bv%2A30=39, for the grams gold result
u%2A10%2Bv%2A40=68, for the grams lead result

The system would be easiest to solve if multiply the gold 39 equation by 2, and then subtract the lead 68 equation from it. This would very quickly give a value for v.