To determine which graph represents the situation regarding the sales of caps and T-shirts, we can set up the problem mathematically.
Let \( x \) be the number of caps sold, and \( y \) be the number of T-shirts sold. Based on the information provided:
- Each cap sells for $5, so the total revenue from caps is \( 5x \).
- Each T-shirt sells for $10, so the total revenue from T-shirts is \( 10y \).
The junior class needs to generate at least $500 in sales, so the inequality can be set up as follows:
\[ 5x + 10y \geq 500 \]
We can simplify this inequality by dividing all terms by 5:
\[ x + 2y \geq 100 \]
This inequality describes a region on the coordinate plane bounded by the line \( x + 2y = 100 \). The area above this line represents the solutions to the inequality, indicating combinations of caps and T-shirts that yield sales of $500 or more.
To identify the correct graph, look for the following characteristics:
- A line labeled \( x + 2y = 100 \).
- The region above this line must be shaded (including all points where sales are greater than or equal to $500).
Without seeing the specific graphs J, K, L, and M, you would look for these features to determine which graph correctly represents the sales situation for the Orvis Ring High School junior class. If you can provide more details about what graphs J, K, L, and M look like, I can help you analyze them!
3 answers