At the movie theatre, child admission is $6.20 and adult admission is$ 9.70. On Monday, twice as many adult tickets as child tickets were sold, for a total sales of $614.40. How many child tickets were sold that day?
Let's call the number of child tickets sold "C" and the number of adult tickets sold "A".
We know that adult tickets cost $9.70 and twice as many adult tickets were sold as child tickets, so we can set up the equation:
A = 2C
We also know that the total sales for the day were $614.40, so we can set up another equation:
6.2C + 9.7A = 614.4
Now we can substitute the first equation into the second equation:
6.2C + 9.7(2C) = 614.4
Simplifying this, we get:
6.2C + 19.4C = 614.4
25.6C = 614.4
C = 24
Therefore, 24 child tickets were sold on Monday.
Let's assume the number of child tickets sold is 'x'.
Since the number of adult tickets sold is twice as many as child tickets, the number of adult tickets sold is 2x.
Now, let's calculate the total revenue from child tickets:
Total revenue from child tickets = child admission rate x number of child tickets
Total revenue from child tickets = $6.20 * x
Similarly, let's calculate the total revenue from adult tickets:
Total revenue from adult tickets = adult admission rate x number of adult tickets
Total revenue from adult tickets = $9.70 * 2x
The total sales for the day is given as $614.40, so we can set up the equation:
Total revenue from child tickets + Total revenue from adult tickets = Total sales
$6.20 * x + $9.70 * 2x = $614.40
Now we can solve for 'x':
6.20x + 9.70(2x) = 614.40
6.20x + 19.40x = 614.40
25.60x = 614.40
x = 614.40 / 25.60
x ≈ 24
Therefore, 24 child tickets were sold on Monday.