One week, a cake shop sold 45 pineapple cakes and 62 chocolate cakes on the weekdays and 55 pineapple cakes and 79 chocolate cakes over the weekend. total sales were $3,520 on the weekdays and $4,415 over the weekend. form a linear system representing this data and create a matrix.

Let us assume cost of each pineapple cake = $x.

Cost of each chocolate cakes = $y.

On weekdays 45 pineapple cakes and 62 chocolate cakes were sold.

Total cost of 45 pineapple cakes and 62 chocolate cakes were sold =  $3,520.

Therefore, first equation would be

45x + 62y = 3520  --------------equation(1).

On weekends 55 pineapple cakes and 79 chocolate cakes were sold.

Total cost of 55 pineapple cakes and 79 chocolate cakes were sold =  $4,415.

Therefore, second equation would be

55x + 79y = 4415   --------------equation(2).

Therefore, system of equation are 45x + 62y = 3520  and 55x + 79y = 4415.And we can form a matrix as

.

Let us assume cost of each pineapple cake = $x.

Cost of each chocolate cakes = $y.

On weekdays 45 pineapple cakes and 62 chocolate cakes were sold.

Total cost of 45 pineapple cakes and 62 chocolate cakes were sold =  $3,520.

Therefore, first equation would be

45x + 62y = 3520  equation(1).

On weekends 55 pineapple cakes and 79 chocolate cakes were sold.

Total cost of 55 pineapple cakes and 79 chocolate cakes were sold =  $4,415.

Therefore, second equation would be

55x + 79y = 4415   equation(2).

Therefore, system of equation are 45x + 62y = 3520  and 55x + 79y = 4415.

And we can form a matrix as

.

Step-by-step explanation:

The determinant of the matrix for the pineapple cake is $4350 ⇒  c

The determinant of the matrix for the chocolate cake is $5075 ⇒  c

Step-by-step explanation:

* Look to the attached file

The determinant of the matrix for the the pineapple cake is 4,350. the price of one pineapple cake is 3,520

The determinant of the matrix for the chocolate cake is 5,075 . the price of the chocolate cake is 4,414

The determinant of the matrix for the pineapple cake is:

The price of one pineapple cake is $ 30 The determinant of the matrix for the chocolate cake is:

The price of one chocolate cake is $ 35Step-by-step explanation:

Let the price of one pineapple cake is: $ x

and the price of one chocolate cake is: $ y

Now, 45 pineapple cakes and 62 chocolate cakes on the weekdays.

such that total sales were $3,520 on the weekdays.

This means the equation that can be formed is:

                      45x+62y=3520

Also, 55 pineapple cakes and 79 chocolate cakes over the weekend.

Total sales on weekend were $ 4415

This means that the equation is given by:

                 55x+79y=4415

Hence, we can form a system as:

     

where

Determinant of A is:

and

Hence, the matrix of the pineapple cake is given by:

and its determinant is given by:

and the price of the pineapple cake is given by:

The matrix of the chocolate cake is given by:

and its determinant is given by:

and the price of one chocolate cake is given by:

The determinant of the matrix for the pineapple cake is

4,350. The price of one pineapple cake is $30.

The determinant of the matrix for the chocolate cake is

5,075. The price of one chocolate cake is $35.