Question

The manager of a theater wants to know whether the majority of its patrons are adults or children. One day, 5200 tickets were sold and the receipts totaled $24,761. The adult admission is 6.50, and the childrenis admission is $3.50. How many adult patrons were there?

Answer 1

There were 2187 adult patrons.

Explanation:

We can solve this problem by assuming the number of adult patrons as 'x'. Framing equations in 'x' and solving them should give us its value.

So, let's observe the given information in order to frame the required equations.

We know that the total number of tickets sold is 5200. This means the sum of the number of adult and child patrons is 5200.

i.e. number of adult patrons + number of child patrons = 5200

So, x + number of child patrons = 5200

This gives us, number of child patrons = 5200 - x

We know that the receipts totaled $24,761. This means the sum of the money from adult admissions and child admissions is $24,761.

Now, if each adult pays $6.50, total collection from x adults will be $6.50x.

Similarly, the total collection from (5200 - x) children will be $3.50(5200 - x).

Based on this, we can say that:

6.50x + 3.50(5200 - x) = 24,761

Solving the above equation gives us:

x = 2187

This means, there were 2187 adult patrons.