Question

Molly is an insurance agent. She is mailing packages filled with marketing items to a few of her clients. The items she is including are pens that weigh x ounces, notepads that weigh y ounces, and magnets that weigh z ounces:

A package filled with 3 pens, 2 notepads, and 1 magnet weighs 8 ounces.
A package filled with 2 pens, 1 notepad, and 2 magnets weighs 3.9 ounces.
A package filled with 4 pens and 3 magnets weighs 4 ounces.
Which matrix equation can be solved to find the weight of each item?

Answer 1

Based on the following information;

A package filled with 3 pens, 2 notepads, and 1 magnet weighs 8 ounces.

A package filled with 2 pens, 1 notepad, and 2 magnets weighs 3.9 ounces.

A package filled with 4 pens and 3 magnets weighs 4 ounces.

Option B can be solved to find the weight of each item

Which matrix equation can be solved to find the weight of each item?

Let's assign variables to represent the weight of each item:

Let x represent the weight of a pen in ounces.

Let y represent the weight of a notepad in ounces.

Let z represent the weight of a magnet in ounces.

We can set up a matrix equation using the given information:

Let A be the coefficient matrix:

3 2 1

2 1 2

4 0 3

Let X be the variable matrix:

x

y

z

And let B be the constant matrix:

8

3.9

4

The matrix equation can be written as AX = B.

Solving this equation will give us the weight of each item (the values of x, y, and z).