At a movie theater, the price of a child’s ticket is $9 and the price of an adult’s ticket is $12. On Friday, the theater sold 820 tickets total and made $9,222. Create a matrix equation to represent the system, using x to represent the number of children’s tickets sold and y to represent the number of adults’ tickets sold.

Question

23-08-2022
Advanced Placement (AP)

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At a movie theater, the price of a child’s ticket is $9 and the price of an adult’s ticket is $12. On Friday, the theater sold 820 tickets total and made $9,222. Create a matrix equation to represent the system, using x to represent the number of children’s tickets sold and y to represent the number of adults’ tickets sold.

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abiolataiwo2015 abiolataiwo2015 · Answer 1 · 2022-08-24T20:11:46+02:00

The matrix equation to represent the system, using x to represent the number of children’s tickets sold and y to represent the number of adults’ tickets sold is: Option C.

Matrix

Given:

Child ticket=$9

Adult ticket=$12

Total ticket sold=820 ticket

Total earnings=$9,222

Let x represent Child ticket and let y represent adult ticket

Hence:

x+y=820...... (1)

9x+12y=9,222......(2)

Matrix representation of equation 1 and 2

[tex]\left[\begin{array}{ccc}1&1\\9&12\\&&\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}x\\y&\\\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}820\\9,222\\\end{array}\right][/tex]

Therefore the matrix equation to represent the system, using x to represent the number of children’s tickets sold and y to represent the number of adults’ tickets sold is: Option C.

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