The Math Club sold slices of pizza, p, at a profit of $3 each and cans of soda, 8, 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)

Question

Equation to represent the total number of items sold _ = 200

Equation to represent the total profit _ = 550

Answer 1

To model the situation with linear equations, we can set up the following variables:

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

We know from the problem statement that:

1. The total number of items (slices of pizza and cans of soda) sold is 200.
2. The total profit made from selling these items is $550.

Now, let's formulate the equations:

1. Equation for total items sold: \[ p + s = 200 \]

2. Equation for total profit:

   • The profit from selling pizza slices is \( 3p \) (since they make a profit of $3 per slice).
   • The profit from selling cans of soda is \( 2s \) (since they make a profit of $2 per can).
   • Therefore, the equation for total profit is: \[ 3p + 2s = 550 \]

Putting it all together, the pair of linear equations that model this situation is:

\[ \begin{align*}

1. & \quad p + s = 200 \
2. & \quad 3p + 2s = 550 \end{align*} \]