A paper company needs to ship paper to a large printing business. The paper will be shipped in small boxes and large boxes. The volume of each small box is 9 cubic feet and the volume of each large box is 24 cubic feet. A total of 24 boxes of paper were shipped with a combined volume of 441 cubic feet. Write a system of equations that could be used to determine the number of small boxes shipped and the number of large boxes shipped. Define the variables that you use to write the system.

Question

A paper company needs to ship paper to a large printing business. The paper will be shipped in small boxes and large boxes. The volume of each small box is 9 cubic feet and the volume of each large box is 24 cubic feet. A total of 24 boxes of paper were shipped with a combined volume of 441 cubic feet. Write a system of equations that could be used to determine the number of small boxes shipped and the number of large boxes shipped. Define the variables that you use to write the system.

Answer 1

Let's define the variables:

Let's call the number of small boxes shipped as "x".
Let's call the number of large boxes shipped as "y".

The volume of each small box is given as 9 cubic feet, so the total volume of the small boxes can be calculated as 9x.
Similarly, the volume of each large box is given as 24 cubic feet, so the total volume of the large boxes can be calculated as 24y.

The total combined volume of all the boxes is given as 441 cubic feet.

Using the above information, we can write the following system of equations:

Equation 1: The total number of small boxes shipped multiplied by the volume of each small box should be equal to the total volume of the small boxes.
9x = Total volume of small boxes

Equation 2: The total number of large boxes shipped multiplied by the volume of each large box should be equal to the total volume of the large boxes.
24y = Total volume of large boxes

Equation 3: The total combined volume of all the boxes should be equal to the sum of the total volumes of the small boxes and the large boxes.
Total volume of small boxes + Total volume of large boxes = 441

So, the system of equations is:
9x = Total volume of small boxes
24y = Total volume of large boxes
Total volume of small boxes + Total volume of large boxes = 441

Answer 2

To write a system of equations that could be used to determine the number of small boxes and large boxes shipped, we can define the variables as follows:

Let's use:
- x to represent the number of small boxes shipped
- y to represent the number of large boxes shipped

To determine the number of small boxes and large boxes shipped, we need to consider the volume of each box and the total combined volume of the boxes.

The volume of each small box is 9 cubic feet, so the total volume of small boxes shipped would be 9x cubic feet.

The volume of each large box is 24 cubic feet, so the total volume of large boxes shipped would be 24y cubic feet.

Since a total of 24 boxes were shipped, we can create the following equation to represent the total number of boxes:

x + y = 24

Next, we need to consider the total combined volume of the boxes, which is given as 441 cubic feet. We can create the following equation to represent the total volume:

9x + 24y = 441

Therefore, the system of equations that could be used to determine the number of small boxes shipped (x) and the number of large boxes shipped (y) is:

x + y = 24
9x + 24y = 441

Answer 3

x+y = 24

9x+24y = 441
Now do your magic.