Question

a chef can spend at least $150 but no more than $252 to prepare a seafood dish for his club. the seafood itself costs $17 per pound, and the total cost of the vegetables required is $48. which graph represents the number of pounds, p, of seafood that the chef can purchase?
(three number lines are shown as images: first from 3 to 14 with endpoints at 6 and 12; second from 3 to 14 with endpoints at 5 and 11; third from 3 to 14 with endpoints at 7 and 10)

Explanation:

Step1: Set up the inequality

The total cost is the cost of seafood plus the cost of vegetables. The cost of seafood is \(17p\) (where \(p\) is the number of pounds) and the cost of vegetables is \(48\). The total cost \(C\) satisfies \(150\leq C\leq252\). So, \(150\leq17p + 48\leq252\).

Step2: Solve the left - hand side of the inequality

Subtract \(48\) from all parts: \(150-48\leq17p+48 - 48\leq252-48\).
\(102\leq17p\leq204\).
Divide all parts by \(17\): \(\frac{102}{17}\leq\frac{17p}{17}\leq\frac{204}{17}\).
\(6\leq p\leq12\).

Answer:

The graph with endpoints at \(6\) and \(12\) (the first graph in the original problem's options, assuming the first graph has filled - in circles at \(6\) and \(12\) and a line segment between them) represents the number of pounds of seafood the chef can purchase.