Question

a chef can spend at least $137 but no more than $251 to prepare a seafood dish for his club. the seafood itself costs $19 per pound, and the total cost of the vegetables required is $42. which graph represents the number of pounds, p, of seafood that the chef can purchase? four number line graphs are shown with different markings at 5,6,7,10,11,12 etc.

Explanation:

Step1: Define the cost inequality

Let \( P \) be the pounds of seafood. The total cost is seafood cost (\( 19P \)) plus vegetable cost (\( 42 \)), so the inequality is \( 137 \leq 19P + 42 \leq 251 \).

Step2: Solve the left inequality

Subtract 42 from all parts: \( 137 - 42 \leq 19P \leq 251 - 42 \)
\( 95 \leq 19P \)
Divide by 19: \( \frac{95}{19} \leq P \)
\( 5 \leq P \)

Step3: Solve the right inequality

\( 19P \leq 209 \)
Divide by 19: \( P \leq \frac{209}{19} \)
\( P \leq 11 \)

Step4: Interpret the solution

The solution \( 5 \leq P \leq 11 \) means the graph should have a closed circle at 5, a closed circle at 11, and the line between them. Looking at the options, the third graph (with closed circles at 5 and 11, shading between) matches.

Answer:

The graph with closed circles at 5 and 11, and the line segment between them (the third option among the given number lines).