To analyze this situation mathematically, let's define the variables:
- Let \( x \) be the number of caps sold.
- Let \( y \) be the number of T-shirts sold.
The revenue generated from selling caps and T-shirts can be expressed as:
\[ 5x + 10y \geq 500 \]
To make the inequality easier to analyze, we can simplify it:
\[ x + 2y \geq 100 \]
Now, let's interpret what this equation represents:
- The line \( x + 2y = 100 \) represents the boundary condition where the total sales exactly equal $500.
- The region above this line (including the line itself) represents all combinations of caps and T-shirts sold that will result in total sales of at least $500.
To represent this situation graphically:
- The x-axis would represent the number of caps sold.
- The y-axis would represent the number of T-shirts sold.
- The line \( x + 2y = 100 \) will slope downwards, intercepting the axes at \( (100, 0) \) and \( (0, 50) \).
To choose from the options provided (J, K, L, M), you would want to select the graph that features a line corresponding to the equation \( x + 2y = 100 \) with the shaded region above this line.
Since I do not have visual access to the graphs listed, I recommend checking for:
- A downward sloping line intersecting the axes at 100 (for caps) and 50 (for T-shirts).
- Shading above the line to represent all combinations of caps and T-shirts that meet or exceed $500.
From that analysis, you should be able to determine which of the options (J, K, L, M) correctly represents this scenario. If you can describe the graphs, I could help you further narrow down the correct one.
3 answers