Abakery sells muffins for $3.50 each. a beverage is $1.75. a class purchases 32 items and spends a total of $87.50.
a. define your variables. write the system of equations and represent it as a matrix equation.
b. state the value of determinant
c. use matrices to solve the system. find the number of muffins and the number of beverages purchased.

For the answer to the question above.
Given:
muffins = 3.50
beverage = 1.75
total number of items = 32
total cost = 87.50

m + b = 32
3.50m + 1.75b = 87.50

m = 32 - b

3.50(32-b) + 1.75b = 87.50
112 - 3.50b + 1.75b = 87.50
-3.50b + 1.75b = 87.50 - 112
-1.75b = -24.50
b = -24.50 / -1.75
b = 14

m = 32 - b
m = 18

The class bought 18 muffins and 14 beverages.

3.50m + 1.75b = 87.50
3.50(18) + 1.75(14) = 87.50
63 + 24.50 = 87.50
87.50 = 87.50