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o-na [289]
3 years ago
6

A movie theater has a seating capacity of 271. The theater charges $5.00 for children, $7.00 for students,

Mathematics
1 answer:
nirvana33 [79]3 years ago
6 0

Answer:

Children attended = 154

Students attended = 40

Adults attended = 77

Step-by-step explanation:

Seating capacity = 271

Charges for each children ticket = $5

Charges for each student ticket = $7

Charges for each adult ticket = $12

Let number of children tickets = 2x

Ticket price for children = \$ 2x \times 5

As per question statement, there were half as many adults as there are children,

so number of adult tickets = x

Ticket price for adults = \$ x \times 12

Now, number of students =

(271-x-2x)\\\Rightarrow (271-3x)

Ticket price for students = \$ (271-3x) \times 7

Total ticket sales = $1974

\Rightarrow 12x+2x\times 5 +(271-3x)\times 7 = 1974\\\Rightarrow 22x-21x +(271 \times 7) = 1974\\\Rightarrow x = 1974 - 1897\\\Rightarrow x = 77

So, number of adults attended = 77

number of children attended = 77 \times 2 = 154

number of students attended = 271 - 77 - 154 = 40

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