Question

Three adult and three child movie tickets were purchased 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 an equation: 3(x+x-3)=75 , where æ represents the cost of an adult ticket. Identify the next step, which would simplify the equation before solving for the variable

a. Divide 75 by 3.
b. Add 3 to 75
c. Combine like terms in parentheses.
d. Distribute values over the variables

Answer 1

The next step is to combine like terms within the parentheses of the equation 3(x + x - 3) = 75, leading to the choice c. Combine like terms in parentheses. Option C is the correct answer.

Step-by-step explanation:

The question asks for the next step in simplifying the equation 3(x + x - 3) = 75 to solve for the cost of an adult movie ticket, where x represents the cost of an adult ticket, and a child's ticket is $3 less.

The proper next step, after writing the equation, is to combine like terms within the parentheses. Combining like terms is critical before performing any other operations because it simplifies the equation and reduces the possibility of errors later in the problem-solving process. Therefore, the correct choice is c. Combine like terms in parentheses. After combining the terms, you would proceed to distribute and solve for x.

The combined like terms would look like this: 3(2x - 3) = 75. Now we can continue solving the problem by distributing the 3 across the terms within the parentheses, resulting in 6x - 9 = 75.

After the distribution is complete, the subsequent steps would be to add 9 to both sides of the equation, and then divide by 6 to find the value of x, which is the cost of an adult ticket. The final answer is c. Combine like terms in parentheses.