Question

At the arcade, Sami won 2 blue tickets, 1 yellow ticket, and 3 red tickets for 1500 total points. Jamie won 1 blue ticket, 2 yellow tickets, and 2 red tickets for 1225 total points. Yvonne won 2 blue tickets, 3 yellow tickets, and 1 red ticket for 1200 total points. Write a system of equations to represent this situation. Let b = point value of blue tickets; y = point value of yellow tickets; r = point value of red tickets Create a matrix for your system.

Answer 1

`\left[\begin{array}{ccc}2&1&3\\1&2&2\\2&3&1\end{array}\right]`
`\left[\begin{array}{c}b&y&r\end{array}\right]`
`= \left[\begin{array}{c}1500&1225&1200\end{array}\right]`

Explanation:

Given

`b = blue`

`y = yellow`

`r = red`

Required

Represent as a matrix

For Sammy:

`2\ blue + 1\ yellow + 3\ red =1500`

So, we have:

`2b + 1y + 3r = 1500`

`2b + y + 3r = 1500`

For Jamie:

`1\ blue + 2\ yellow + 2\ red =1225`

So, we have:

`1b + 2y + 2r = 1225`

`b + 2y + 2r = 1225`

For Yvonne:

`2\ blue + 3\ yellow + 1\ red =1200`

So, we have:

`2b + 3y + 1r = 1200`

`2b + 3y + r = 1200`

The system of equations are:

`2b + y + 3r = 1500`

`b + 2y + 2r = 1225`

`2b + 3y + r = 1200`

To represent as a matrix, we have:

`\left[\begin{array}{ccc}b_1&y_1&r_1\\b_2&y_2&r_2\\b_3&y_3&r_3\end{array}\right]`
`\left[\begin{array}{c}b&y&r\end{array}\right]`
`= \left[\begin{array}{c}Total_1&Total_2&Total_3\end{array}\right]`

This gives:

`\left[\begin{array}{ccc}2&1&3\\1&2&2\\2&3&1\end{array}\right]`
`\left[\begin{array}{c}b&y&r\end{array}\right]`
`= \left[\begin{array}{c}1500&1225&1200\end{array}\right]`