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. what is the pair of linear equations that model this situation.
Let's start by defining our variables:
p = number of slices of pizza sold
s = number of cans of soda sold
We know that the Math Club sold a total of 200 items, so we can write one equation:
p + s = 200
We also know that the profit from selling each slice of pizza is $3, and the profit from selling each can of soda is $2. If we multiply the number of slices of pizza sold (p) by 3, and add that to the profit from the cans of soda sold (s x 2), we get the total profit:
3p + 2s = 550
Therefore, the pair of linear equations that model this situation are:
p + s = 200
3p + 2s = 550
Let's use the following variables:
p = number of slices of pizza sold
s = number of cans of soda sold
The profit from selling slices of pizza is $3 each, so the total profit from slices of pizza sold is 3p.
The profit from selling cans of soda is $2 each, so the total profit from cans of soda sold is 2s.
The total number of items sold is 200, so the equation for the total number of items is p + s = 200.
The total profit is $550, so the equation for the total profit is 3p + 2s = 550.
Therefore, the pair of linear equations that model this situation is:
p + s = 200
3p + 2s = 550.
To model this situation with linear equations, let's define the variables:
p = number of pizza slices sold
s = number of cans of soda sold
Given that the Math Club sold 200 items, we can create the first equation:
p + s = 200 -- Equation 1
Since each pizza slice was sold at a profit of $3 and each can of soda at a profit of $2, the total profit can be represented by the equation:
3p + 2s = 550 -- Equation 2
Thus, the pair of linear equations that model this situation are:
1. p + s = 200
2. 3p + 2s = 550