Question

I just need help setting it up and graphing :)

Answer 1

9x+15y=270

• (0,18): 0 short-sleeved shirts and 18 long-sleeved shirts.

,

• (30,0): 30 short-sleeved shirts and 0 long-sleeved shirts.

,

• (10,12): 10 short-sleeved shirts and 12 long-sleeved shirts.

Explanation:

Let the number of short-sleeved t-shirts sold = x

Let the number of long-sleeved t-shirts sold = y

• A Short-sleeved t-shirt costs $9, therefore x t-shirts costs $9x

,

• A long-sleeved t-shirt costs $15, therefore y t-shirts cost $15y

,

• At the game, she made $270.

An equation that represents the number of sales during the period is:

`9x+15y=270`

Next, the line is graphed.

First, find the intercepts.

`\begin{gathered} \text{When }x=0 \\ 9(0)+15y=270 \\ \implies15y=270 \\ \implies y=18 \\ \text{When y}=0 \\ 9x+15(0)=270 \\ \implies9x=270 \\ \implies x=30 \end{gathered}`

The intercepts are (0,18) and (30, 0).

The graph is attached below:

Three different combinations of shirts that could have been sold are:

0. (0,18): 0 short-sleeved shirts and 18 long-sleeved shirts.

,

1. (30,0): 30 short-sleeved shirts and 0 long-sleeved shirts.

,

2. (10,12): 10 short-sleeved shirts and 12 long-sleeved shirts.