Question

Pedro owns a shrimp truck near the beach. He sells garlic shrimp for $8 a plate and spicy shrimp for $6 a plate. Each day Pedro stocks enough shrimp to sell at most 120 plates total, but he would like to earn at least $800. Which combination of garlic shrimp plates and spicy shrimp plates can Pedro sell to meet his goal? A. 15 garlic shrimp plates and 110 spicy shrimp plates B. 80 garlic shrimp plates and 20 spicy shrimp plates C. 90 garlic shrimp plates and 25 spicy shrimp plates D. 70 garlic shrimp plates and 55 spicy shrimp plates

Answer 1

To meet his goal of earning at least $800, Pedro can sell either 15 garlic shrimp plates and 110 spicy shrimp plates, 90 garlic shrimp plates and 25 spicy shrimp plates, or 70 garlic shrimp plates and 55 spicy shrimp plates.

Step-by-step explanation:

In order to meet his goal of earning at least $800, Pedro needs to find a combination of garlic shrimp plates and spicy shrimp plates that will yield a total revenue of at least $800.

Let x be the number of garlic shrimp plates and y be the number of spicy shrimp plates.

The total revenue can be calculated using the equation: 8x + 6y ≥ 800.

We also know that the total number of plates cannot exceed 120, so we have the constraint: x + y ≤ 120.

We can solve this system of inequalities to find the valid combinations:

Option A: 15 garlic shrimp plates and 110 spicy shrimp plates. Revenue: 8(15) + 6(110) = 870. This option meets the revenue goal and the plate constraint.

Option B: 80 garlic shrimp plates and 20 spicy shrimp plates. Revenue: 8(80) + 6(20) = 840. This option meets the revenue goal and the plate constraint.

Option C: 90 garlic shrimp plates and 25 spicy shrimp plates. Revenue: 8(90) + 6(25) = 870. This option meets the revenue goal and the plate constraint.

Option D: 70 garlic shrimp plates and 55 spicy shrimp plates. Revenue: 8(70) + 6(55) = 870. This option meets the revenue goal and the plate constraint.

Therefore, options A, C, and D are valid combinations for Pedro to meet his goal.

Answer 2

C

Step-by-step explanation:

You can plug in each combination to see what would work

C is the only combination that satisfies all the constraints: it earns him more than $800 and is less than 120 plates.