To find the ratio of the number of adult tickets to the total number of tickets, we start by calculating the number of adult tickets sold.
Given that the total number of tickets sold is 78 and the number of child tickets sold is 48, we can find the number of adult tickets as follows:
\[ \text{Number of adult tickets} = \text{Total tickets} - \text{Child tickets} = 78 - 48 = 30 \]
Now we have:
- Number of adult tickets = 30
- Total number of tickets = 78
Next, we need to establish the ratio of the number of adult tickets to the total number of tickets:
\[ \text{Ratio of adult tickets to total tickets} = \frac{\text{Adult tickets}}{\text{Total tickets}} = \frac{30}{78} \]
To express this as a ratio, we can simplify the fraction. First, we find the greatest common divisor (GCD) of 30 and 78. The GCD is 6.
Now, we simplify the fraction:
\[ \frac{30 \div 6}{78 \div 6} = \frac{5}{13} \]
Thus, the ratio of the number of adult tickets to the total number of tickets is:
\[ 5 : 13 \]
Therefore, the final answer is:
\[ \boxed{5:13} \]
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