Question

Ryan, Michelle, and Erwin spent $13.50, $16.50, and $14, respectively, at an amusement park. Ryan bought three tickets for the Ferris wheel and two tickets for the water slide. Michelle bought one ticket for the Ferris wheel and four tickets for the merry-go-round. Erwin bought three tickets for the Ferris wheel, one ticket for the water slide, and one ticket for the merry-go-round. Let x, y, and z represent the ticket cost for the Ferris wheel, water slide, and merry-go-round, respectively. Identify the column entries that belong in the matrix equation that models this situation, A-1B = X.

Answer 1

To model the given situation in a matrix equation, we set up matrices A, B, and X using the given information. The equation A-1B = X represents the relationship between these matrices.

Step-by-step explanation:

In this problem, we are given the amounts spent by Ryan, Michelle, and Erwin at an amusement park. We are also given the number of tickets they bought for each ride. Let x, y, and z represent the ticket cost for the Ferris wheel, water slide, and merry-go-round, respectively. To create a matrix equation that models this situation, we need to set up the matrices A, B, and X as follows:

A = [[3, 2, 0], [1, 0, 4], [3, 1, 1]], B = [[x], [y], [z]], X = [[13.50], [16.50], [14]].

The equation A-1B = X represents the multiplication of the inverse of matrix A with matrix B, which is equal to matrix X.

Answer 2

This photo should be pretty clear on how to answer.

Step-by-step explanation: