Question

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.

Answer 1

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.

Answer 2

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

`\left[\begin{array}{ccc}45&62&3520\\55&79&4415\end{array}\right]`.