SOLUTION: A chemist has two alloys, one of which is 5% gold and 15% lead and the other which is 20% 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 571924: A chemist has two alloys, one of which is 5% gold and 15% lead and the other which is 20% gold and 40% lead. How many grams of each of the two alloys should be used to make an alloy that contains 31 g of gold and 85 g of lead?
You can put this solution on YOUR website! A chemist has two alloys, one of which is 5% gold and 15% lead and the other which is 20% gold and 40% lead.
How many grams of each of the two alloys should be used to make an alloy that contains 31 g of gold and 85 g of lead?
:
Let x = amt of 1st alloy, Let y = amt of the 2nd alloy (in grams)
:
Gold equation: .05x + .20y = 31
Lead equation: .15x + .40y = 85
:
Multiply the 1st equation by 2, subtract from the 2nd equation
.15x + .40y = 85
.10x + .40y = 62
---------------------
.05x + 0y = 23
x =
x = 460 grams of the 1st alloy
:
then using the 1st equation to find y
.05(460) + .2y = 31
23 + .2y = 31
.2y = 31 - 23
y =
y = 40 grams of the 2nd alloy
:
:
Check these solutions in the 2nd original equation
.15(460) + .40(40) =
69 + 16 = 85
