To solve this problem, let's denote the number of adult tickets as [tex]\( a \)[/tex].
1. Define the given relationship:
The number of child tickets is [tex]\(\frac{3}{5}\)[/tex] of the number of adult tickets. Hence, the number of child tickets is [tex]\(\frac{3}{5}a\)[/tex].
2. Define the cost components:
- Each child ticket costs [tex]$\$[/tex] 5[tex]$.
- Each adult ticket costs $[/tex]\[tex]$ 8$[/tex].
3. Calculate the total revenue:
The total revenue from child tickets can be expressed as:
[tex]\[
5 \cdot \frac{3}{5}a = 3a
\][/tex]
The total revenue from adult tickets can be expressed as:
[tex]\[
8a
\][/tex]
4. Set up the equation for the total revenue, which is given as \$ 550:
[tex]\[
3a + 8a = 550
\][/tex]
5. Combine like terms and solve for [tex]\( a \)[/tex]:
[tex]\[
11a = 550
\][/tex]
[tex]\[
a = \frac{550}{11} = 50
\][/tex]
Therefore, there are 50 adult tickets sold.
6. Determine the number of child tickets:
Since the number of child tickets [tex]\( c \)[/tex] is [tex]\(\frac{3}{5}\)[/tex] of the number of adult tickets:
[tex]\[
c = \frac{3}{5} \times 50 = 30
\][/tex]
So, the number of child tickets sold is [tex]\( \boxed{30} \)[/tex].
