sean ordered lunch from the hamburger hut for everyone on the baseball team he bought either a slice of pizza or a hamburger for all 32 people on the team and he spent $124,00. the hamburger hut gave sean 50% off each slice of pizza that was order with a hamburger. the regular price of each hamburger is $5.00 and the regular price of each slice of pizza is $4.00. later when asked what he bought sean said he purchased 15 hamburgers and 17 slices of pizza is this possible given the above information?

Question

sean ordered lunch from the hamburger hut for everyone on the baseball team he bought either a slice of pizza or a hamburger for all 32 people on the team and he spent $124,00. the hamburger hut gave sean 50% off each slice of pizza that was order with a hamburger. the regular price of each hamburger is $5.00 and the regular price of each slice of pizza is $4.00. later when asked what he bought sean said he purchased 15 hamburgers and 17 slices of pizza is this possible given the above information?

Answer 1

Let x be the number of hamburgers purchased and y be the number of slices of pizza purchased.

From the given information, we have the following equations:
x + y = 32 (total number of people on the team)
5x + 4y = 124 (total amount spent)

We can also express the total cost of the order with the discount for slices of pizza that were ordered with a hamburger:
5(15) + 3.5(17) = 124 (total amount spent with discount included)

Solving the equations simultaneously:
x + y = 32
5x + 4y = 124

Multiplying the first equation by 4:
4x + 4y = 128

Subtracting the second equation from the modified first equation:
(4x + 4y) - (5x + 4y) = 128 - 124
-x = 4
x = -4

From the negative value of x, it is clear that the numbers given by Sean are not possible. Therefore, Sean cannot have purchased 15 hamburgers and 17 slices of pizza as stated.