# The manager of a theater wants to know whether the majority of its patrons are adults or children. One​ day, 5300 tickets were sol

Question

The manager of a theater wants to know whether the majority of its patrons are adults or children. One​ day, 5300 tickets were sold and the receipts totaled ​\$22,906. The adult admission is ​\$5.50​, and the​ children’s admission is ​\$3.50. How many adult patrons were​ there?

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1 month 2022-12-24T17:09:20+00:00 1 Answer 0 views 0

1. There 4,828 adult patrons in the theater
What is simultaneous equations?
Simultaneous equations are two or more equations that are related and are solved together, in essence, the solutions to unknowns in one equation are related to the unknowns in other equations.
In this case, we can assume that the number of adults is A, whereas the number children is C, in essence, the total number of attendees are determined thus:
A+C=5300…………(equation 1)
The total revenue earned is determined thus:
\$5.50A+\$3.50C=\$22,906………..(equation 2)
From equation 1, we can solve for C in terms of A
C=5300-A
substitute for C in equation 2
\$5.50A+\$3.50(5300-A)=\$22,906
\$5.50A+\$13,250-\$3.50A=\$22,906
\$2.00A+\$13,250=\$22,906
\$2.00A=\$22,906-\$13,250
\$2.00A=\$9656
A=\$9656/\$2.00