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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. Identify the first step if solving this problem arithmetically, which would find the cost of one adult and one child ticket.

7 answers

To solve the problem arithmetically, the first step would be to define variables for the costs of the adult and child movie tickets. Let's define:

  • Let \( A \) be the cost of one adult ticket.
  • Let \( C \) be the cost of one child ticket.

According to the problem, we know two things:

  1. The total cost for three adult tickets and three child tickets is $75, which can be expressed as: \[ 3A + 3C = 75 \]

  2. The cost of each child ticket is $3 less than the cost of an adult ticket, which can be written as: \[ C = A - 3 \]

The next steps would then involve substituting the second equation into the first equation to solve for either \( A \) or \( C \). But the very first step is defining the variables \( A \) and \( C \).

3 of 5 3 of 5 Items

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. Identify the first step if solving this problem arithmetically, which would find the cost of one adult and one child ticket.

Add 3 to 75.

Divide 75 by 3.

Divide 75 by 6.

Subtract 6 from 75.

The first step if solving this problem arithmetically, which would help find the cost of one adult and one child ticket, is to divide 75 by 6.

Here’s why:

  1. You have a total of 3 adult tickets and 3 child tickets, which makes a total of 6 tickets.
  2. If you divide the total amount of $75 by the total number of tickets (6), you can find the average price per ticket, which will help you set up the equations to find the individual costs of adult and child tickets.

Thus, the correct first step is to divide 75 by 6.

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 x
represents the cost of an adult ticket. Identify the next step, which would simplify the equation before solving for the variable. (1 point)
Responses

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

The next step to simplify the equation \( 3(x + (x - 3)) = 75 \) would be to combine like terms in parentheses.

This means you should first simplify the expression inside the parentheses before moving on to distributing or solving for the variable.

So, when you combine \( x + (x - 3) \), this simplifies to \( 2x - 3 \). The equation would then be

\[ 3(2x - 3) = 75. \]

After this step, you can proceed with distributing to further simplify the equation.

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. Find the price of each ticket.(1 point)
Responses

an adult ticket is $11 and a child ticket is $8
an adult ticket is $11 and a child ticket is $8
an adult ticket is $8 and a child ticket is $5
an adult ticket is $8 and a child ticket is $5
an adult ticket is $14 and a child ticket is $11
an adult ticket is $14 and a child ticket is $11
an adult ticket is $12.50 and a child ticket is $9.50

To find the price of each ticket, let's solve the equations step by step.

  1. Let \( A \) represent the cost of an adult ticket and \( C \) represent the cost of a child ticket. According to the problem:

    • The total cost of 3 adult and 3 child tickets is $75: \[ 3A + 3C = 75. \]
    • The cost of each child ticket is $3 less than the cost of an adult ticket: \[ C = A - 3. \]

  2. Substitute the second equation into the first equation: \[ 3A + 3(A - 3) = 75. \]

  3. Simplifying this: \[ 3A + 3A - 9 = 75, \] \[ 6A - 9 = 75. \]

  4. Add 9 to both sides: \[ 6A = 84. \]

  5. Divide by 6 to solve for \( A \): \[ A = 14. \]

  6. Now, plug \( A \) back into the equation for \( C \): \[ C = A - 3 = 14 - 3 = 11. \]

Thus, the price of each ticket is:

  • An adult ticket is $14.
  • A child ticket is $11.

So the correct response is an adult ticket is $14 and a child ticket is $11.