Question

Brian is making 12 pounds of nut mixture with almonds and hazelnut. almonds cost $10.80 per pound and hazel nuts cost $10.20 per pound. How many pounds of almonds and how many pounds of hazelnut should Brian use for the mixture to cost $10.35 per pound to make?

Answer 1

Using a system of equations, Brian should use 3 pounds of almonds and 9 pounds of hazelnut to make the mixture.

What is a system of equations?

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are:

• Variable x: Number of pounds of almonds.

• Variable y: Number of pounds of hazelnut.

Considering that he makes 12 pounds, at a price of 12 x 10.35 = $124.2, the equations are given as follows:

• x + y = 12.

• 10.8x + 10.2y = 124.2.

From the first equation, y = 12 - x, hence, replacing in the second:

10.8x + 10.2y = 124.2

10.8x + 10.2(12 - x) = 124.2

0.6x = 1.8

x = 1.8/0.6

x = 3

y = 12 - x = 12 - 3 = 9.

Brian should use 3 pounds of almonds and 9 pounds of hazelnut to make the mixture.

More can be learned about a system of equations at https://brainly.com/question/24342899

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