SOLUTION: A chemist has two alloys, one of which is 15% gold and 25% 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 all

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A chemist has two alloys, one of which is 15% gold and 25% 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 all      Log On


   

Question 672545: A chemist has two alloys, one of which is 15% gold and 25% 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 74 g of gold and 126 g of lead?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A chemist has two alloys, one of which is 15% gold and 25% 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 74 g of gold and 126 g of lead?
:
The x = amt of the 1st alloy
let y = amt of the 2nd alloy
:
Write a mixture equation for each amt:
gold percent
.15x + .20y = 74
the lead percent
.25x + .40y = 126
:
multiply the 1st equation by 2, subtract the 2nd equation
.30x + .40y = 148
.25x + .40y = 126
--------------------subtraction eliminates y, find x
.05x = 22
x = 22%2F.05
x = 440 grams of the 1st alloy
:
Find y using the 1st original equation (gold)
.15(440) + .20y = 74
66 + .20y = 74
.20y = 74 - 66
.20y = 8
y = 8/.2
y = 40 grams of the 2nd alloy
:
:
See if that checks out in lead equation
.25(440) + .40(40) = 126
110 + 16 = 126
:
We can see we need 440 grams of the 1st alloy and 40 grams of the 2nd