Question

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)

Answer 1

Complete Question: The complete question is in the file attached to this solution

Answer:

a)
`\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]`

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

Explanation:

The matrix vector equation can be written as:

`A \bar{X} = B`............(1)

let X₁ = Price of small drinks

Let X₂ = Price of medium drinks

The vector
`\bar{X}` of the prices of small and medium drinks is:

`\bar{X} = \left[\begin{array}{ccc}X_(1) \\X_(2) \end{array}\right]`

The matrix of the total sales can be written as:

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

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

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

`\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]`

`45X_(1) + 24X_(2) = 155.25\\67X_(1) + 89X_(2) = 397.80`

Solving for X₁ and X₂ in the equations above:

X₁ = 1.78

X₂ = 3.13