Question

Customer A spent $18 on a plate of brisket, two sides, and a drink. Customer B spent $10 on a plate of brisket and a drink. Customer C spent $57 on three plates of brisket, six sides, and four drinks. Which augmented matrix best represents the system of linear equations that could be used to determine the price of each item?

A) [1 2 1 | 18; 1 0 1 | 10; 3 6 4 | 57]
B) [1 1 3 | 18; 0 1 6 | 10; 1 1 4 | 57]
C) [18 10 57 | 1; 2 1 6 | 0; 1 1 4 | 3]
D) [1 1 1 | 18; 1 0 0 | 10; 1 1 1 | 57]

Answer 1

The correct augmented matrix for determining the price of each item is A) [1 2 1 | 18; 1 0 1 | 10; 3 6 4 | 57], representing a system of equations for the number of briskets, sides, and drinks purchased by each customer.

Step-by-step explanation:

The correct augmented matrix that represents the system of linear equations to determine the price of each item is A) [1 2 1 | 18; 1 0 1 | 10; 3 6 4 | 57]. This matrix corresponds to the system where the first column represents the number of plates of brisket, the second column represents the number of sides, and the third column represents the number of drinks. The number following the vertical bar in each row is the total amount spent by each customer.

Let's define the variables as follows: 'b' for the price of a plate of brisket, 's' for the price of a side, and 'd' for the price of a drink. The equations generated from the information given in the question would be:

• b + 2s + d = $18 (Customer A)
• b + 0s + d = $10 (Customer B)
• 3b + 6s + 4d = $57 (Customer C)