word problem

Question

A metallurgist has one alloy containing 42% aluminum and another containing 64% aluminum. How many pounds of each alloy must he use to make 45 pounds of a third alloy containing 51% aluminum? (Round to two decimal places if necessary.)

Answer 1

Let x = the number of pounds of alloy1 and 45-x = the number of pounds of alloy2.

The final amount of aluminum will be 0.42*x + 0.64*(45-x) = 0.51*45.

⇒  -0.22x + 28.8 = 22.95    ⇒    x = 26.59, 45-x = 18.41

so 26.59 lbs. of alloy1 and 18.41 lbs. of alloy2