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 $2.50 a slice and burritos for $3.00 each. the cafeteria collected a total of $358 for selling these two items. homework help 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.

Explanation:

Part (a)

Step1: Define Variables

Let \( p \) be the number of pizza slices sold and \( b \) be the number of burritos sold.

Step2: First Equation (Quantity Relationship)

The number of pizza slices sold was 20 less than twice the number of burritos sold. So, \( p = 2b - 20 \).

Step3: Second Equation (Cost Relationship)

Pizza slices cost \$2.50 each and burritos cost \$3.00 each, with a total of \$358. So, \( 2.50p + 3.00b = 358 \).

Step1: Substitute \( p \) into Cost Equation

Substitute \( p = 2b - 20 \) into \( 2.50p + 3.00b = 358 \).
\( 2.50(2b - 20) + 3.00b = 358 \)

Step2: Simplify and Solve for \( b \)

Expand: \( 5b - 50 + 3b = 358 \)
Combine like terms: \( 8b - 50 = 358 \)
Add 50 to both sides: \( 8b = 408 \)
Divide by 8: \( b = 51 \)

Step3: Solve for \( p \)

Substitute \( b = 51 \) into \( p = 2b - 20 \).
\( p = 2(51) - 20 = 102 - 20 = 82 \)

Answer:

Let \( p \) = number of pizza slices sold, \( b \) = number of burritos sold.
Equation 1: \( p = 2b - 20 \)
Equation 2: \( 2.50p + 3.00b = 358 \)

Part (b)