SOLUTION: A chemist has two alloys, one of which is 15% gold and 15% 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 al

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Question 719979: A chemist has two alloys, one of which is 15% gold and 15% 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 80.5 g of gold and 76.5 g of lead?
_____ g (first alloy)
_____ g (second alloy)
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Summary of given information:
First alloy: 15% Gold, 15% Lead.
Second alloy: 40% Gold, 30% Lead.
WANT NEW ALLOY containing 80.5 grams Gold and 76.5 grams Lead.

Let x = grams of first alloy
Let y = grams of second alloy

Account for Gold: 0.15x%2B0.40y=80.5+
Account for Lead: 0.15x%2B0.30y=76.5
Those two, when multiplied by 100 and then divided by 5 give the equivalent system,
highlight%283x%2B8y=1610%29
highlight%283x%2B6y=1530%29

In that form, the second equation can be subtracted from the first equation and the result solved for y, giving the grams of the "second alloy" to use. Next, use either equation of this system to find the value of x, the "first alloy" to use.