SOLUTION: A chemist has two alloys, one of which is 15% gold and 10% lead and the other which is 20% gold and 30% lead. How many grams of each of the two alloys should be used to make an all

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: A chemist has two alloys, one of which is 15% gold and 10% lead and the other which is 20% gold and 30% lead. How many grams of each of the two alloys should be used to make an all      Log On


   

Question 1073596: A chemist has two alloys, one of which is 15% gold and 10% lead and the other which is 20% gold and 30% lead. How many grams of each of the two alloys should be used to make an alloy that contains 82.5 g of gold and 65 g of lead?
g (first alloy)
g (second alloy)
Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=grams of alloy1 (15% gold, 10%lead)
And let y=grams of alloy2(20% gold, 30% lead)
Total of amount of gold:
0.15x+0.20y=82.5 Eq1
Total amount of lead:
0.10x+0.30y=65 Eq2
Sooooo
0.15x+0.20y=82.5
0.10x+0.30y=65
Multiply eq1 by 2 and eq2 by3 and we get:
0.30x+0.40y=165 eq1a
0.30x+0.90y=195 eq2a
subtract eq1a from eq2a and we get
0.50y=30
y=60 grams amount of alloy 1
substitute 60 gms for y in eq1a
0.30x+24=165
0.30x=141
x=470 grams amount of alloy 2
CK
total amount of gold:
60*0.20+470*0.15=
12+70.5=82.5gms---check
total amount of lead:
60*0.30+470*0.10=
18+47=65gms---check
Hope this helps---ptaylor