Question

At the movies, Devin bought three tickets, one drink, and one bag of popcorn for $43.75. Neil bought one ticket, three drinks, and two bags of popcorn for $27.75. Jung bought two tickets, two drinks, and one bag of popcorn for $34. Make an augmented matrix to represent the situation and use it to find out the prices for one ticket, one drink, and one bag of popcorn.

A. [3, 1, 1 | 43.75; 1, 3, 2 | 27.75; 2, 2, 1 | 34]
B. [3, 1, 1 | 43.75; 1, 3, 2 | 27.75; 2, 2, 1 | 34.25]
C. [3, 1, 1 | 43.75; 1, 3, 2 | 27.75; 2, 2, 1 | 34]
D. [3, 1, 1 | 43.75; 1, 3, 2 | 27.75; 2, 2, 1 | 35]

Answer 1

The augmented matrix that represents the total cost of movie tickets, drinks, and popcorn based on given purchases is A. [3, 1, 1 | 43.75; 1, 3, 2 | 27.75; 2, 2, 1 | 34]. This matrix can be solved using Gaussian elimination to find the individual prices of a ticket, drink, and popcorn.

Step-by-step explanation:

The setting up an augmented matrix to solve a system of equations that represents the total cost of movie tickets, drinks, and bags of popcorn based on the purchases made by Devin, Neil, and Jung. To do this, we represent the number of tickets, drinks, and popcorn as variables and create equations based on the information given.

For Devin, the equation is 3t + 1d + 1p = 43.75, for Neil it is 1t + 3d + 2p = 27.75, and for Jung, it is 2t + 2d + 1p = 34, with t representing the price of one ticket, d the price of one drink, and p the price of one popcorn. The augmented matrix that represents this situation is thus: A. [3, 1, 1 | 43.75; 1, 3, 2 | 27.75; 2, 2, 1 | 34].

Once the matrix is set up, we can use methods such as Gaussian elimination to solve for the values of t, d, and p, which will give us the prices of one ticket, one drink, and one bag of popcorn.