Systems of Linear Equations Unit Test

Question

11 of 1411 of 14 Items

Question
The Math Club sold slices of pizza, p
, at a profit of $3 each and cans of soda, s
, at $2 each to raise money for a trip. They sold 200 items and made a profit of $550. Write the pair of linear equations that model this situation.(1 point)
Equation to represent the total number of items sold:
= 200
Equation to represent the total profit:
= 550

Answer 1

To model the situation with a pair of linear equations, we can define the variables as follows:

• Let \( p \) be the number of slices of pizza sold.
• Let \( s \) be the number of cans of soda sold.

Given the information:

1. The total number of items sold (slices of pizza and cans of soda) is 200.
2. The profit made from each slice of pizza is $3, and the profit from each can of soda is $2, leading to a total profit of $550.

From this information, we can write the following pair of linear equations:

1. For the total number of items sold: \[ p + s = 200 \]

2. For the total profit: \[ 3p + 2s = 550 \]

So, the two equations that model the situation are:

1. \( p + s = 200 \)
2. \( 3p + 2s = 550 \)