Question

Tania purchased P packages of pasta for $1.25 each and J jars of sauce for $1.85 each. She purchased 22 items and spent $33.50. Which system of equations could be used to determine how many of each item Tania purchased? ​

Answer 1

The student's scenario with Tania's shopping can be solved using a system of linear equations, where P + J = 22 and 1.25P + 1.85J = 33.50 represent the total number of items and the total amount spent, respectively.

Step-by-step explanation:

Tania's shopping can be represented by a system of linear equations based on the number of items purchased and the total cost. The first equation would account for the total quantity of items (packages of pasta and jars of sauce), while the second equation would represent the total cost of these items. With P representing the number of packages of pasta and J representing the number of jars of sauce, the system is:

• P + J = 22 (for the total number of items)
• 1.25P + 1.85J = 33.50 (for the total amount spent)

This system of equations can be solved using methods such as substitution or elimination to find the values of P and J.