It is a fairly long word problem.

Question

A 480-pound alloy containing 30% silver was mixed with an alloy containing 55% silver to get an alloy containing 40% silver. how many pounds of the 55% alloy were used?

Answer 1

Hello, Cynthia,

Let's start with how much silver (Ag) is in the 480 lb alloy with 30%Ag. That is 480*0.30 = 144 lbs. The amount of silver added per pound of the second alloy, at 55% is (0.55 lb Ag)/lb alloy.

The final alloy is 40% silver, so we can construct a formula reflecting the amount of silver going into this sample with the following equation, where X is the pounds of the second (55%) alloy:

144 lbs Ag + 0.55*X lbs Ag = Total lb Ag

The total silver content is divided by the total weight of the 40% alloy to give us the percentage Ag in the alloy, which we want to be 40%.

So take the formula for total Ag above and divide it by the total weight, which is 480 lbs + X and set that equal to 0.40.

We get: (144 lbs Ag + 0.55X lbs Ag)/(480 lbs + X) = 0.40

144 + 0.55X = 192 + 0.40X

0.15X = 48

X = 320 lbs.

Check the answer:

Bob