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

Answer:

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

Step-by-step 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:

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