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 hte pair of linear equations that model this situation.

1 answer

To model this situation with a pair of linear equations, we can define two variables:

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

We have two key pieces of information:

  1. The total number of items (pizza slices and soda cans) sold is 200. This gives us our first equation: \[ p + s = 200 \]

  2. The profit made from selling the pizza slices and soda cans is $550. The profit from each slice of pizza is $3, and the profit from each can of soda is $2. This gives us our second equation: \[ 3p + 2s = 550 \]

Now we have the following pair of linear equations that model the situation:

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