SOLUTION: Chemistry: a chemist has two alloys, one of which is 10% gold and 15% lead, and the other of which is %30 gold and 40% lead. How many grams of each of the two alloys should be used
Algebra.Com
Question 164616: Chemistry: a chemist has two alloys, one of which is 10% gold and 15% lead, and the other of 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 60g of gold and 88g of lead?
What are the steps to solve this problem?
Answer by gonzo(654) (Show Source): You can put this solution on YOUR website!
let x = amount of grams in first alloy.
let y = amount of grams in second alloy.
-----
question is how many grams of each alloy is needed to make 60 grams of gold and 88 grams of lead.
-----
number of grams of gold in first alloy is .10 * x.
number of grams of gold in second alloy is .30 * y.
-----
number of grams of lead in first alloy is .15 * x.
number of grams of lead in second alloy is .4 * y.
-----
total number of grams of gold in third alloy is 60.
total number of grams of lead in third alloy is 88.
-----
total grams of gold from first and second alloy must = 60.
equation looks like.
.10*x + .30*y = 60
-----
total grams of lead from first and second alloy must = 88.
equation looks like.
.15*x + .4*y = 88
-----
solve these equations simultaneously.
.10*x + .30*y = 60 (first equation)
.15*x + .4*y = 88 (second equation)
multiply both sides of first equation by 1.5
.15*x + .45*y = 90
subtract first equation from second eqution.
.05*y = 2
divide both sides by .05
y = 40
-----
substitute 40 for y in first equation.
.10*x + .30*(40) = 60
.10*x + 12 = 60
.10*x = 48
x = 480
-----
substitute 40 for y and 480 for x in second equation.
.15*480 + .45*40 = 90
72 + 18 = 90
90 = 90
x = 480 and y = 40 looks good in second equation.
-----
answer is you need 480 grams of first alloy and 40 grams of second alloy.
-----
RELATED QUESTIONS
A chemist has two alloys, one of which is 10% gold and 15% lead, and the other of which... (answered by arallie)
A chemist has two alloys, one of which is 15% gold and 15% lead and the other which is... (answered by josgarithmetic)
A chemist has two alloys, one of which is 15% gold and 25% lead and the other which is... (answered by josgarithmetic)
A chemist has two alloys, one of which is 15% gold and 20% lead and the other which is... (answered by ikleyn)
A chemist has two alloys, one of which is 5% gold and 10% lead and the other which is 30% (answered by josgarithmetic)
A chemist has two alloys, one of which is 15% gold and 10% lead and the other which is... (answered by ptaylor)
A chemist has two alloys, one of which is 5% gold and 25% lead and the other which is 40% (answered by ikleyn)
A chemist has two alloys, one of which is 5% gold and 15% lead and the other which is 20% (answered by ankor@dixie-net.com)
A chemist has two alloys, one of which is 15% gold and 25% lead and the other which is... (answered by ankor@dixie-net.com)