Question

Jackie buys 3 hot dogs and 1 pretzel from a restaurant for $12.25. Sylvia buys 2 hot dogs and 4 pretzels from the same restaurant for $16.50. Which system of equations can be used to determine the price of a hot dog, h, and a pretzel, p, at the restaurant?

a) 3h + p = 12.25, 2h + 4p = 16.50
b) 3h + 4p = 12.25, 2h + p = 16.50
c) h + 3p = 12.25, 4h + 2p = 16.50
d) 4h + 2p = 12.25, h + 3p = 16.50

Answer 1

The correct system of equations to determine the price of a hot dog, h, and a pretzel, p, based on the purchases made by Jackie and Sylvia is 3h + p = 12.25 and 2h + 4p = 16.50 (option a).

Step-by-step explanation:

To determine the price of a hot dog, h, and the price of a pretzel, p, we can set up a system of equations based on the information provided. Jackie's purchase of 3 hot dogs and 1 pretzel for $12.25 is represented by the equation 3h + p = 12.25. Sylvia's purchase of 2 hot dogs and 4 pretzels for $16.50 is represented by the equation 2h + 4p = 16.50. Therefore, the correct system of equations that can be used to determine the prices is option (a): 3h + p = 12.25, 2h + 4p = 16.50. This system of equations can be solved using methods such as substitution, elimination, or graphing.