Question

Three adult and three child movie ticket were ur chased for $75. The cost of each child ticket is $3 less than the cost of an adult ticket. The first step to solving this problem algebraically is to write ean equation: 3 ( x + x 3 ) = 75, where x represents the cost of an adult ticket. Identify the nest step, which would simplify the equation before solving for the variable.

Combine like terms in parentheses

Divide 75 by 3

Distribute values over the variables

Add 3 to 75

Answer 1

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:

1. **Distribute the values over the variables**:
\[
3x + 3(x - 3) = 75 \implies 3x + 3x - 9 = 75
\]

2. Combine the like terms:
\[
6x - 9 = 75
\]

Thus, the next step after writing the initial equation is to **distribute values over the variables**.