To solve the problem, we need to find the cost of one adult ticket (let's call it \( A \)) and one child ticket (let's call it \( C \)). We know that three adult tickets and three child tickets cost $75, and that the cost of a child ticket is $3 less than the cost of an adult ticket.
We can set up the following equations based on the information given:
- \( 3A + 3C = 75 \) (total cost of tickets)
- \( C = A - 3 \) (cost relationship between adult and child tickets)
From the first equation, we can simplify it by dividing everything by 3:
\[ A + C = 25 \]
Now, we can substitute the second equation into this equation:
\[ A + (A - 3) = 25 \] \[ 2A - 3 = 25 \] \[ 2A = 28 \] \[ A = 14 \]
Now, substitute back to find \( C \):
\[ C = A - 3 = 14 - 3 = 11 \]
So the cost of one adult ticket is $14, and the cost of one child ticket is $11.
Now, the question asks for the first step if solving this problem arithmetically, which would directly help us find the cost of one adult and one child ticket.
Given the options:
A. Divide 75 by 6
B. Add 3 to 75
C. Subtract 6 from 75
D. Divide 75 by 3
The most logical first step to frame this problem and eventually find \( A \) and \( C \) would be Option D: Divide 75 by 3. This would lead to the average cost per adult and child ticket combined, which aligns with our simplified equation \( A + C = 25 \).
Thus, the answer is D. Divide 75 by 3.