Question

A bakery 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.

Answer 1

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