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. (2 points)

Question

Equation to represent the total number of items sold blank one = 200.
Equation to represent the total profit blank 2 =550

Blank-1 p + 3, 3s, p + s
Blank 2 3p + 20s, 2p + 3s, p + s

Answer 1

To create the pair of linear equations that model this situation, we need to define the relationships based on the information given about the sales of pizza slices and cans of soda.

Let:

• \( p \) = number of pizza slices sold
• \( s \) = number of cans of soda sold

1. Equation to represent the total number of items sold (200 items): This can be expressed as: \[ p + s = 200 \]

2. Equation to represent the total profit ($550): The profit from pizza slices is \( 3p \) (since they make $3 profit per pizza slice) and the profit from soda is \( 2s \) (since they make $2 profit per can of soda). Therefore, the total profit equation is: \[ 3p + 2s = 550 \]

So, the pair of linear equations is:

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