Question

A paper company needs to ship paper to a large printing business. The paper will beshipped in small boxes and large boxes. Each small box of paper weighs 25 poundsand each large box of paper weighs 50 pounds. There were 4 more large boxesshipped than small boxes and the total weight of all boxes was 800 pounds.Graphically solve a system of equations in order to determine the number of smallboxes shipped, 2, and the number of large boxes shipped, y.

Answer 1

The number of small boxes is represented by x and the number of large boxes is represented by y.

If each small box weighs 25 pounds, the large box weighs 50 pounds, and the total weight is 800 pounds, then we have:

`\begin{gathered} 25x+50y=800 \\ Dividing\text{ }through\text{ }by\text{ }25: \\ x+2y=32\text{ ---------------------\lparen1\rparen} \end{gathered}`

If there are 4 more large boxes than small boxes, we have the relationship to be:

`x+4=y\text{ ---------------\lparen2\rparen}`

We can plot the graphs using the intercepts of the equations.

Intercepts for Equation 1

At x = 0:

`\begin{gathered} 2y=32 \\ y=16 \end{gathered}`

At y = 0:

`x=32`

The points are (0, 16) and (32, 0).

Intercepts for Equation 2

At x = 0:

`y=4`

At y = 0:

`\begin{gathered} x+4=0 \\ x=-4 \end{gathered}`

The points are (0, 4) and (-4, 0).

Using the above points, we have the graph as shown below:

The solution to the equations is the point of intersection. This is at:

`(x,y)=(8,12)`

Therefore, the solution to the question is:

`\begin{gathered} x=8 \\ y=12 \end{gathered}`

Hence, there are 8 small boxes and 12 large boxes.