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Inessa05 [86]
3 years ago
12

The Cinema Center consists of four theaters: Cinemas I, II, III, and IV. The admission price for one feature at the Center is $5

for children, $7 for students, and $9 for adults. The attendance for the Sunday matinee is given by the matrixChildren - Students - AdultsCinema I - 225 - 110 - 70Cinema II - 95 - 160 - 225Cinema III - 280 - 65 - 110Cinema IV - 0 - 240 - 225a. Write a column vector B representing the admission prices.b. Compute AB, the column vector showing the gross receipts for each theater.c. Find the total revenue collected at the Cinema Center for admission that Sunday afternoon.
Mathematics
1 answer:
zzz [600]3 years ago
3 0

Answer:

a) Matrix B = \left[\begin{array}{c}5\\7\\9\end{array}\right]

b) Matrix AB = \left[\begin{array}{c}2525\\3620\\2845\\3705\end{array}\right]

c) $12,695

Step-by-step explanation:

Matrix A = \left[\begin{array}{ccc}225&110&70\\95&160&225\\280&65&110\\0&240&225\end{array}\right]

a) Matrix B = \left[\begin{array}{c}5\\7\\9\end{array}\right]

Gross Receipt = AB

\left[\begin{array}{ccc}225&110&70\\95&160&225\\280&65&110\\0&240&225\end{array}\right] . \left[\begin{array}{c}5\\7\\9\end{array}\right] = \left[\begin{array}{c}2525\\3620\\2845\\3705\end{array}\right]

c) Total revenue is the sum of receipts from 4 cinemas given in part b

Hence,

Total revenue = $2525 + $3620 + $2845 + $3705 = $12,695

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Step-by-step explanation:

You don't have to go far to find the equations. They are right there in your problem statement. Perhaps you want to find the solutions to the equations.

Use the first equation to write an expression for x, then substitute that into the second equation:

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