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

Solve a system of linear equations to find the amount of 42% and 64% aluminum alloys needed to make 45 pounds of a 51% aluminum alloy. Algebraic methods such as substitution or elimination will be used.

Step-by-step explanation:

The metallurgist question is about creating a new alloy with a specific percentage of aluminum by mixing two alloys with different aluminum contents. We're solving a system of linear equations to determine the amount of each alloy needed to create 45 pounds of a new alloy with 51% aluminum.

Let x be the amount of the alloy with 42% aluminum, and y be the amount of the alloy with 64% aluminum. The system of equations then is:

1. 0.42x + 0.64y = 0.51 × 45
2. x + y = 45

Solving this system gives us the quantities of each alloy to mix. Once we find the values of x and y, we will have the answer to how many pounds of each alloy the metallurgist must use. These calculations will involve using algebraic methods such as substitution or elimination.