To solve the problem algebraically, the first step identified is to write the equation:
\[ 3(x + x - 3) = 75 \]
Where \( x \) represents the cost of an adult ticket. However, the correct formulation should reflect the relationship between the adult and child ticket prices.
The cost of a child ticket is \( x - 3 \). The correct equation representing the total cost of the tickets would be:
\[ 3x + 3(x - 3) = 75 \]
Now, simplifying this:
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Distribute the values over the variables: \[ 3x + 3(x - 3) = 75 \implies 3x + 3x - 9 = 75 \]
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Combine the like terms: \[ 6x - 9 = 75 \]
Thus, the next step after writing the initial equation is to distribute values over the variables.