Question

4-62

On Tuesday the cafeteria sold pizza slices and burritos. The number of pizza slices sold was 20 less than twice the number of burritos sold. Pizza sold for $2.50 a slice and burritos for $3.00 each. The cafeteria collected a total of $358 for selling these two items
a. Write two equations with two variables to represent the information in this problem. Be sure to define your variables
b.Solve the system from part (a). Then determine how many pizza slices were sold.

Answer 1

After defining the number of pizza slices as 'p' and the number of burritos as 'b', the equations p = 2b - 20 and 2.50p + 3b = 358 were created and solved to find that 82 pizza slices were sold.

Step-by-step explanation:

The question asks for writing a system of equations and solving it to determine how many pizza slices and burritos were sold, given the prices of each and the total sales. The variables can be defined as follows: let p be the number of pizza slices sold, and b be the number of burritos sold.

Part a: System of Equations

The first equation represents the relationship between the number of pizza slices and burritos sold:
p = 2b - 20
The second equation represents the total sales from both items:
2.50p + 3b = 358

Part b: Solving the System

Substitute the first equation into the second:
2.50(2b - 20) + 3b = 358
5b - 50 + 3b = 358
8b - 50 = 358
8b = 408
b = 51
Now, substituting back to find p:
p = 2(51) - 20
p = 102 - 20
p = 82

Therefore, 82 pizza slices were sold.