MATH SOLVE

3 months ago

Q:
# 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.

Accepted Solution

A:

The matrix equation that represents this situation is

[tex] \left[\begin{array}{ccc}3&2&0\\1&0&4\\3&1&1\end{array}\right]*\left[\begin{array}{ccc}x\\y\\z\end{array}\right]=\left[\begin{array}{ccc}13.50\\16.50\\14.00\end{array}\right] [/tex]

Use technology to find the inverse of matrix A:

[tex]A^{-1}= \left[\begin{array}{ccc}-\frac{2}{5}&-\frac{1}{5}&\frac{4}{5}\\ \frac{11}{10}&\frac{3}{10}&-\frac{6}{5}\\\frac{1}{10}&\frac{3}{10}&-\frac{1}{5}\end{array}\right] [/tex]

Multiplying A inverse by B, we get the solution matrix

[tex]\left[\begin{array}{ccc}2.50\\3\\3.50\end{array}\right][\tex]

[tex] \left[\begin{array}{ccc}3&2&0\\1&0&4\\3&1&1\end{array}\right]*\left[\begin{array}{ccc}x\\y\\z\end{array}\right]=\left[\begin{array}{ccc}13.50\\16.50\\14.00\end{array}\right] [/tex]

Use technology to find the inverse of matrix A:

[tex]A^{-1}= \left[\begin{array}{ccc}-\frac{2}{5}&-\frac{1}{5}&\frac{4}{5}\\ \frac{11}{10}&\frac{3}{10}&-\frac{6}{5}\\\frac{1}{10}&\frac{3}{10}&-\frac{1}{5}\end{array}\right] [/tex]

Multiplying A inverse by B, we get the solution matrix

[tex]\left[\begin{array}{ccc}2.50\\3\\3.50\end{array}\right][\tex]