Tickets to a school play were $5 for adults and $3 for students. A total of 247 tickets were sold for a profit of $1000. How many adult tickets an student tickets were sold?
5 a + 3 s = 1000
a+s = 247 so s = (247-a)
5 a + 3(247-a) = 1000
5 a + 741 - 3 a = 1000
2 a = 259
a = 129.5 humm, poorly stated question?
s = 117.5
To solve this problem, we can start by setting up a system of equations. Let's call the number of adult tickets sold as 'a', and the number of student tickets sold as 's'.
Based on the given information, we can write two equations:
Equation 1: a + s = 247 (total number of tickets sold)
Equation 2: 5a + 3s = 1000 (total profit generated)
Now we can solve this system of equations to find the values of 'a' and 's'.
Let's solve Equation 1 for 'a':
a = 247 - s
Substituting this value of 'a' into Equation 2:
5(247 - s) + 3s = 1000
1235 - 5s + 3s = 1000
1235 - 2s = 1000
-2s = 1000 - 1235
-2s = -235
s = -235 / -2
s = 117.5
Since the number of tickets must be a whole number, we can see that s = 117 is a reasonable value.
Now that we have s = 117, we can substitute it back into Equation 1 to find 'a':
a = 247 - 117
a = 130
So, 130 adult tickets and 117 student tickets were sold.