Three adult and three child movie tickets were purchased for $75. for the cost of each child ticket is $3 less than the cost of the adult tickets. Identify the first step if solving this problem arithmetically, which would find the cost of one adult and one child ticket.
A) divide 75 by 3
B) add 3 to 75
C) subtract 6 from 75
D) divide 7 by 6
The correct option is D) divide 7 by 6.
To find the cost of one adult and one child ticket arithmetically, we need to set up an equation using the given information. Let's denote the cost of one adult ticket as "A" and the cost of one child ticket as "C".
From the problem, we know that three adult tickets and three child tickets were purchased for a total of $75. We also know that the cost of each child ticket is $3 less than the cost of each adult ticket.
So, we can set up the equation:
3A + 3C = 75.
Since the cost of each child ticket is $3 less than the cost of each adult ticket, we can express that as C = A - 3.
Now, we can substitute C = A - 3 into the equation:
3A + 3(A - 3) = 75.
Simplifying the equation, we get:
6A - 9 = 75.
Adding 9 to both sides of the equation, we get:
6A = 84.
Finally, dividing both sides of the equation by 6, we get:
A = 14.
Therefore, the cost of one adult ticket is $14. To find the cost of one child ticket, we substitute A = 14 into C = A - 3:
C = 14 - 3,
C = 11.
So, the cost of one child ticket is $11.