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.
Define your variables. Write the system of equations and represent it as a matrix equation.
State the value of the determinant.
Use matrices to solve the system. Find the number of muffins and the number of beverages purchased.

Answer 1

The prices mentioned in the question connect to the variables

Use a variables for muffins and beverages

You were asked to make 2 equations. A hint here is to create one for price and another for amount of items bought

Answer 2

...no comment

Answer 3

tbh that doesn't help my slow self.

Answer 4

Do you know what variables are?

Answer 5

yes, they are x y z etc.

Answer 6

so x for muffins and y for beverages?

Answer 7

I meant in the question but yes youre right

Answer 8

smh-

Answer 9

if you let x = # of muffins and y = # of beverages

the amount of $$ spent on muffins is (price of muffins)(number of muffins)

same logic w/ the beverages. (price of beverages)(number of beverages)

adding the amt spent on beverages + muffins will give you the total cost

plugging in the appropriate values, 3.5x + 1.75y = 87.5

Answer 10

the class purchases 32 items, so x + y = 32

your system:

3.5x + 1.75y = 87.5
x + y = 32

now to convert this to matrix form simply write a 2x2 matrix with the coefficients 3.5, 1.75, 1, and 1 in that order

multiply that by a 2x1 matrix with items x and y

write an equals sign

then another 2x1 matrix with the constants 87.5 and 32

Answer 11

the determinant of the 2x2 coefficient matrix is simply

Answer 12

solving the system:

first find the inverse of the coefficient matrix A


where |A| is the determinant from the previous step

multiply both sides of the system by the inverse matrix ***important*** the inverse matrix must be written on the left on both sides, a.k.a

A^(-1) * A [x,y] = A^(-1) [constant matrix]

the inverse cancels out with A and you just have [x,y] = solution matrix