Tickets are being sold for a theater. Cost for students: 2 dollars. Cost for other people: 5 dollars. The total amount of tickets sold: 250. Total amount of money made: 950. How many of the tickets were sold to the students? To the others?
2 s + 5 a = 950
s+a = 250 so a = 250 - s
2 s + 5 (250-s) = 950
To solve this problem, we can use a system of equations. Let's assign variables to the unknowns:
Let's say x represents the number of tickets sold to students.
And let's say y represents the number of tickets sold to other people.
We are given the following information:
1. The cost for students is $2 per ticket.
2. The cost for other people is $5 per ticket.
3. The total number of tickets sold is 250.
4. The total amount of money made is $950.
Based on this information, we can set up two equations:
Equation 1: x + y = 250 (since the total number of tickets sold is 250)
Equation 2: 2x + 5y = 950 (since the total amount of money made is $950)
To solve this system of equations, we can use the substitution method or the elimination method. Let's use the substitution method.
From Equation 1, we can isolate x:
x = 250 - y
Now, substitute this value of x into Equation 2:
2(250 - y) + 5y = 950
Distribute the 2:
500 - 2y + 5y = 950
Combine like terms:
3y = 450
Divide by 3:
y = 150
Now that we have the value of y, we can substitute it back into Equation 1 to find x:
x + 150 = 250
Subtract 150 from both sides:
x = 100
Therefore, 100 tickets were sold to students and 150 tickets were sold to other people.