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. using elimination

Question

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. using elimination

Answer 1

Let:

m = number of muffins sold
c = number of cookies sold

The system of equations representing the situation is:
11m + 6c = 540
m + c = 55

To solve using elimination, we can multiply the second equation by 6 to make the coefficients of "c" the same:
6m + 6c = 330

Now, we can subtract the modified second equation from the first equation to eliminate "c":
11m + 6c - 6m - 6c = 540 - 330
5m = 210
m = 42

Now we can plug in the value of m into the second equation to solve for c:
42 + c = 55
c = 13

Therefore, the ordered pair that satisfies the system of equations is (42, 13). This means that the school sold 42 muffins and 13 cookies on Day 1 of the fundraiser.