Question

The manager of a theater wants to know whether the majority of its patrons were adults or children. one day 5100 tickets were sold in the receipts totaled 34,599. The adult admission is $8.50 and the children’s admission is $5.50. How many adult patrons were there?

Answer 1

Answer:

Adults 2183

Children 2917

Step-by-step explanation:

Let adult tickets be x and children's ticket be y

Using the total sold tickets then

X+y=5100

Making x the subject tjen X=5100-y

Using the amount collected then

8.5x+ 5.5y=34599

8.5(5100-y)+5.5y=34599

43350-8.5y+5.5y=34599

3y=8751

y=2917

X=5100-y=5100-2917=2183

x=2183

Therefore, adults were 2183 and children 2917

Answer 2

So there were 2183 adults.

Let there are x adults and y children.

So, x + y = 5100 .....(1)

8.50x + 5.50y = 34599 ....(2)

From x + y = 5100 we get y = 5100 - x.

Then from (2) we get:

$8.50x + 5.50y = 34599\\8.50x + 5.50(5100-x) = 34599\\x=2183$

So, y = 5100 - x = 5100 - 2183 = 2917

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