Question

Manuel is buying salad and pizza for a company lunch. Suppose that a bowl of salad costs $5.00, and a slice of pizza costs $2.00.

Let E be the amount in dollars that Manuel spends on salad and pizza. If Manuel buys S bowls of salad and P slices of pizza, then the total amount of money he spends (E) can be represented by the equation ____.
Now rearrange the equation you wrote above so that P is written in terms of E and S. The quantity of pizza he buys can be represented by the equation ______.
Suppose Manuel has $40.00 to spend on salad and pizza; that is, E = $40.00.
Complete the following table with the values of Sor P that make the equation true.
Hint: To complete the first row, determine the number of pizza slices Manuel can purchase with $40.00, when the number of salad bowls he purchases is 0.
Budget (Dollars) Salad (Bowls) Pizza (Slices)
40.00 0 ____
40.00 4 ____
40.00 _____ 0

Answer 1

Manuel's spending on salad and pizza is captured by the equation E = 5S + 2P. Rearranging for P gives P = (E - 5S) / 2. Using a $40 budget, we can determine the possible combinations of salads and pizzas.

Step-by-step explanation:

Manuel's total spending on salad and pizza, represented by E, can be determined by the following equation which represents a budget constraint:

E = 5S + 2P

Where S is the number of salad bowls at $5 each, and P is the number of pizza slices at $2 each. To express the number of pizza slices P in terms of the total amount spent E and the number of salad bowls S, we rearrange the equation:

P = (E - 5S) / 2

If Manuel has $40.00 to spend, the values for the number of salad bowls (S) and pizza slices (P) that make the equation true are calculated as follows:

• For S = 0, then P = (40 - 5×0) / 2 = 20 slices of pizza.
• For S = 4, then P = (40 - 5×4) / 2 = 10 slices of pizza.
• For S = 8 (maximal number of salads), then P = (40 - 5×8) / 2 = 0 slices of pizza, as all money is spent on salad.