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.

Question

16-01-2021
Mathematics

contestada

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.

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MrRoyal MrRoyal · Answer 1 · 2021-01-21T03:53:07+01:00

Answer:

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

Step-by-step explanation:

Given

[tex]b = blue[/tex]

[tex]y = yellow[/tex]

[tex]r = red[/tex]

Required

Represent as a matrix

For Sammy:

[tex]2\ blue + 1\ yellow + 3\ red =1500[/tex]

So, we have:

[tex]2b + 1y + 3r = 1500[/tex]

[tex]2b + y + 3r = 1500[/tex]

For Jamie:

[tex]1\ blue + 2\ yellow + 2\ red =1225[/tex]

So, we have:

[tex]1b + 2y + 2r = 1225[/tex]

[tex]b + 2y + 2r = 1225[/tex]

For Yvonne:

[tex]2\ blue + 3\ yellow + 1\ red =1200[/tex]

So, we have:

[tex]2b + 3y + 1r = 1200[/tex]

[tex]2b + 3y + r = 1200[/tex]

The system of equations are:

[tex]2b + y + 3r = 1500[/tex]

[tex]b + 2y + 2r = 1225[/tex]

[tex]2b + 3y + r = 1200[/tex]

To represent as a matrix, we have:

[tex]\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][/tex] [tex]\left[\begin{array}{c}b&y&r\end{array}\right][/tex] [tex]= \left[\begin{array}{c}Total_1&Total_2&Total_3\end{array}\right][/tex]

This gives:

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