A chemist has two alloys, one of which is 10% gold and 20% 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 65 g of gold and 118 g of lead?
A) First alloy: 60 g; second alloy: 470 g
B) First alloy: 470 g; second alloy: 62 g
C) First alloy: 472 g; second alloy: 60 g
D) First alloy: 470 g; second alloy: 60 g
E) None of the above

Question

Quizplus · Accepted Answer

Let x be the amount of the first alloy and y be the amount of the second alloy.

We can set up a system of two equations to represent the problem:

0.1x + 0.3y = 65   (the equation for the amount of gold)
0.2x + 0.4y = 118  (the equation for the amount of lead)

To solve for x and y, we can use any method of solving systems of equations. One common method is to use elimination.

We can multiply the first equation by 2 and subtract it from the second equation to eliminate y:

0.2x + 0.4y = 118
-0.2x - 0.6y = -130
-------------------
0.0x - 0.2y = -12

Solving for y, we get:

y = 60

Substituting y back into either of the original equations, we can solve for x:

0.1x + 0.3y = 65
0.1x + 0.3(60) = 65
0.1x + 18 = 65
0.1x = 47
x = 470

Therefore, we need 470 grams of the first alloy and 60 grams of the second alloy to make an alloy with 65 grams of gold and 118 grams of lead, so the answer is D.

A Chemist Has Two Alloys, One of Which Is 10