the cinema sold 600 tickets total. adults tickets were $15 and childrens tickets were $8. they made a total of $7740. how much of each ticket were sold?
a = number of adults
c = number of childrens
number of adults + number of childrens = 600 total
a + c = 600
a * 15 $ + c * 8 $ = 7740 $
15 a + 8 c = 7740
Now you must solve system of two equations:
a + c = 600
15 a + 8 c = 7740
The solutions are :
a = 420
c = 180
420 adults
and
180 childrens
Proof :
420 * 15 $ + 180 * 8 $ =
6300 $ + 1440 $ = 7440 $
To determine how many adult and children tickets were sold, we can set up a system of equations based on the given information.
Let's assume that the number of adult tickets sold is represented by 'a', and the number of children tickets sold is represented by 'c'.
From the given information, we have two equations:
1. The total number of tickets sold: a + c = 600
2. The total amount of money made from ticket sales: 15a + 8c = 7740
We can solve this system of equations using the substitution method or the elimination method.
Let's use the substitution method:
From equation (1), we can express 'a' in terms of 'c' by rearranging it as: a = 600 - c
Now substitute this expression for 'a' in equation (2):
15(600 - c) + 8c = 7740
Simplify the equation:
9000 - 15c + 8c = 7740
Combine like terms:
-7c = -1260
Divide both sides of the equation by -7:
c = 180
Now substitute the value of 'c' back into equation (1) to find the value of 'a':
a + 180 = 600
a = 420
Therefore, 420 adult tickets and 180 children tickets were sold.