This is because a new hire messed everything up and sold everything at a different cost. If the total amount made from small drinks is $155.25 and the amount made from medium drinks is $397.80. Write a matrix-vector equation to represent the scenario and find out how much the new hire sold small and medium drinks for. (2 pts for equation, 3 pts for solving)

a) [tex]\left[\begin{array}{ccc}45&24\\67&89\end{array}\right] =\left[\begin{array}{ccc}X_{1} \\X_{2} \end{array}\right] + \left[\begin{array}{ccc}155.25 \\397.80 \end{array}\right][/tex]

b) The new hire sold a small drink for $1.78 and a medium drink for $3.13

Step-by-step explanation:

The matrix vector equation can be written as:

[tex]A \bar{X} = B[/tex]............(1)

let X₁ = Price of small drinks

Let X₂ = Price of medium drinks

The vector [tex]\bar{X}[/tex] of the prices of small and medium drinks is:

[tex]\bar{X} = \left[\begin{array}{ccc}X_{1} \\X_{2} \end{array}\right][/tex]

The matrix of the total sales can be written as:

[tex]A = \left[\begin{array}{ccc}45&24\\67&89\end{array}\right][/tex]

[tex]B = \left[\begin{array}{ccc}155.25 \\397.80 \end{array}\right][/tex]

According to the equation written in (1), the matrix vector equation is:

[tex]\left[\begin{array}{ccc}45&24\\67&89\end{array}\right] =\left[\begin{array}{ccc}X_{1} \\X_{2} \end{array}\right] + \left[\begin{array}{ccc}155.25 \\397.80 \end{array}\right][/tex]

[tex]45X_{1} + 24X_{2} = 155.25\\67X_{1} + 89X_{2} = 397.80[/tex]

Solving for X₁ and X₂ in the equations above:

X₁ = 1.78

X₂ = 3.13