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.
Let the number of pizza slices sold be represented by p and the number of cans of soda sold be represented by s.
The profit made from selling pizza slices is $3 per slice, so the profit from p pizza slices is 3p dollars.
The profit made from selling cans of soda is $2 per can, so the profit from s cans of soda is 2s dollars.
According to the given information, the Math Club sold 200 items and made a profit of $550.
This can be written as the equation p + s = 200 and 3p + 2s = 550.
Thus, the pair of linear equations that model this situation are:
p + s = 200
3p + 2s = 550
wrong
My apologies for the mistake.
Let's set up the correct equations to model this situation.
Let x be the number of pizza slices sold, and y be the number of cans of soda sold.
The profit made from selling pizza slices is $3 per slice, so the profit from x pizza slices is 3x dollars.
The profit made from selling cans of soda is $2 per can, so the profit from y cans of soda is 2y dollars.
According to the given information, the Math Club sold 200 items and made a profit of $550.
This can be written as the equation x + y = 200 (since 200 items were sold in total) and 3x + 2y = 550 (since the total profit was $550).
Thus, the correct pair of linear equations that model this situation are:
x + y = 200
3x + 2y = 550
To write the pair of linear equations that model this situation, we need to determine the relationships between the number of pizza slices sold (p) and cans of soda sold (s) with the profit made.
1. Equation for the number of pizza slices sold and the profit:
The Math Club made a profit of $3 for each pizza slice sold, so the equation is:
Profit from pizzas = 3p
2. Equation for the number of cans of soda sold and the profit:
The Math Club made a profit of $2 for each can of soda sold, so the equation is:
Profit from sodas = 2s
3. Equation combining the total number of items sold and the total profit made:
The Math Club sold a total of 200 items, which is the sum of pizza slices and cans of soda. So, the equation is:
Total items sold = p + s
Using the given information that the profit made is $550, we can create another equation:
Total profit = 3p + 2s = 550
Therefore, the pair of linear equations that model this situation are:
3p + 2s = 550 (Equation 1)
p + s = 200 (Equation 2)
These equations can be used to solve for the number of pizza slices and cans of soda sold by the Math Club.