Question

Set up the augmented matrix. Do not solve.4) A basketball fieldhouse seats 15,000. Courtside seats sell for $10, endzone for $6, andbalcony for $4. Total revenue for a sell-out is $82,000. If half the courtside and balconyand all endzone seats are sold, the total revenue is $ 47,000. Set up the augmentedmatrix. Do not solve.

Answer 1

We have the following:

Let c, numbers of courtside seats

let b, numbers of balcony seats

let e, numbers of endzone seats

c + b + e = 15000 (equation 1)

10c + 4b + 6e = 82000 (equation 2)

half the courtside and balcony seats and all the endzone seats are sold, the total revenue is 47000, therefore:

10*0.5c + 4*0.5b + 6e = 47000

5c + 2b + 6e = 47000 (equation 3)

Nwo, the matrix is:

$\begin{bmatrix}{1} & {1} & {1} \\ {10} & {4} & 6 \\ {5} & {2} & {6}\end{bmatrix}=\begin{aligned}15000 \\ 82000 \\ 47000\end{aligned}$