A school is selling muffins and cookies for a fundraiser. ● The school sold each muffin for $11 and each cookie for $6. ● On Day 1 of the fundraiser the school made $540. ● On Day 1 of the fundraiser the school sold 55 total items. Write a system of equations that represents this situation, what ordered pair satisfies that system of equations? Be sure to define variables.
Let:
- \( x \) be the number of muffins sold
- \( y \) be the number of cookies sold
Based on the given information, we can create the following system of equations:
1. \( 11x + 6y = 540 \) (Total revenue from muffins and cookies sold on Day 1 is $540)
2. \( x + y = 55 \) (Total number of items sold on Day 1 is 55)
To find the ordered pair that satisfies this system of equations, we can use the substitution method:
From equation 2, we can express \( x \) as \( 55 - y \) and substitute it to equation 1:
\( 11(55 - y) + 6y = 540 \)
\( 605 - 11y + 6y = 540 \)
\( -5y = -65 \)
\( y = 13 \)
Substitute \( y = 13 \) back to equation 2 to solve for \( x \):
\( x + 13 = 55 \)
\( x = 42 \)
Therefore, the ordered pair that satisfies the system of equations is \( (42, 13) \).