To determine how many outfits and pairs of shoes Jake can pack while adhering to the baggage weight policy, we can create an inequality based on the weights of the outfits and shoes.
Let:
- \( x \) = the number of outfits (each weighs 2 pounds)
- \( y \) = the number of pairs of shoes (each weighs 3 pounds)
The weight policy states that the total weight must be less than 50 pounds. We can express this as:
\[ 2x + 3y < 50 \]
To understand which graph might represent this inequality, we can analyze the boundary line \( 2x + 3y = 50 \) and the region that satisfies the inequality. The graph will depict combinations of \( x \) and \( y \) (the outfits and shoes), and the shaded area representing feasible combinations will be below that line, not touching or exceeding it.
To visualize this:
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Find the intercepts:
- If \( x = 0 \): \( 3y = 50 \) → \( y = \frac{50}{3} \approx 16.67 \)
- If \( y = 0 \): \( 2x = 50 \) → \( x = 25 \)
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The intercepts tell us that the line crosses the x-axis at \( (25, 0) \) and the y-axis at approximately \( (0, 16.67) \).
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The inequality indicates that Jake can pack any combinations of outfits and shoes that lie below this line.
You will need to visually compare the provided options (graphs J, K, L, M) to see which one correctly represents the line \( 2x + 3y = 50 \) and the shaded area below it.
Without the actual graphs to analyze, I can't definitively choose the correct option. However, based on the description above, look for the graph where the line slopes downwards and the area representing valid combinations (under the line) is clearly delineated.
If you can share the representations or characteristics of each graph, I could help you identify which one matches this inequality.