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. (1 point)
Responses:
Divide 75 by 6.
Add 3 to 75.
Subtract 6 from 75.
Divide 75 by 3.
Divide 75 by 3.
Let's solve the equation step by step.
Let x be the cost of an adult ticket.
Then the cost of a child ticket is x - $3.
We can set up the equation:
3x + 3(x - $3) = $75
Simplifying the equation:
3x + 3x - $9 = $75
6x - $9 = $75
Now, isolate the variable x:
6x = $75 + $9
6x = $84
Finally, solve for x by dividing both sides of the equation by 6:
x = $84 / 6
x = $14
Therefore, the cost of an adult ticket is $14.
And the cost of a child ticket is $14 - $3 = $11.
So, the price of each ticket is $14 for adults and $11 for children.
Dividing 75 by 3 would find the cost of one adult and one child ticket because it would evenly distribute the total cost of $75 among the three adult tickets. Since three child tickets are purchased and each child ticket costs $3 less than an adult ticket, the cost of one adult ticket can be found by dividing $75 by 3.
The next step would be to distribute and combine like terms in the equation.
1. Distribute the 3, then add 12, and lastly divide by 3.
2. Multiply by -2
3. Divide 75 by 3
4. Combine
5. Adult $14, child $11