Question

James sold 450 tickets for the community play. Tickets for children cost $2, and tickets for adults cost $5. James sold $1,800 worth of tickets.

How many tickets for adults did James sell?

Enter your answer in the box.

Answer 1

Let the number of children's tickets sold be \( c \) and the number of adult tickets sold be \( a \).

We have the following two equations based on the problem's conditions:

1. The total number of tickets sold:
\[
c + a = 450
\]

2. The total revenue from ticket sales:
\[
2c + 5a = 1800
\]

We can solve these equations step by step.

First, from the first equation, we can express \( c \) in terms of \( a \):
\[
c = 450 - a
\]

Next, we substitute \( c \) in the second equation:
\[
2(450 - a) + 5a = 1800
\]

Expanding this, we get:
\[
900 - 2a + 5a = 1800
\]

Combining like terms:
\[
900 + 3a = 1800
\]

Now, we isolate \( a \):
\[
3a = 1800 - 900
\]
\[
3a = 900
\]
\[
a = \frac{900}{3} = 300
\]

Thus, the number of adult tickets sold is \( \boxed{300} \).

We can also find the number of children's tickets sold for verification:
\[
c = 450 - a = 450 - 300 = 150
\]

Now checking the revenue:
\[
2c + 5a = 2(150) + 5(300) = 300 + 1500 = 1800
\]

The calculations confirm that the solution is correct, and James sold \( \boxed{300} \) adult tickets.