Tickets to a concert cost $12 for adults and $8.50 for students. A total of 950 people paid $10175. How many adults were at the concert
12 a + 8.5 s = 10,175
a+s = 950 so s = (950-a)
12 a + 8.5(950-a) = 10,175
12 a + 8075 - 8.5 a = 10,175
3.5 a = 2100
a = 600
To find the number of adults at the concert, we need to set up a system of equations using the given information.
Let's suppose the number of adults at the concert is represented by the variable "A".
Since each adult ticket costs $12, the total revenue from adult tickets can be calculated as "12A".
Similarly, let's suppose the number of students at the concert is represented by the variable "S".
Since each student ticket costs $8.50, the total revenue from student tickets can be calculated as "8.50S".
We know that the total number of people attended the concert is 950, so we can write the equation:
A + S = 950 -- Equation 1
We also know that the total revenue from ticket sales is $10,175, so we can write the equation:
12A + 8.50S = 10,175 -- Equation 2
Now, we can solve the system of equations using the substitution or elimination method.
Let's choose the elimination method:
Multiplying Equation 1 by -8.50 gives us:
-8.50A - 8.50S = -8,075 -- Equation 3
Adding Equation 2 and Equation 3 eliminates the "S" variable:
12A + 8.50S - 8.50A - 8.50S = 10,175 - 8,075
Simplifying the equation:
3.50A = 2,100
Dividing both sides by 3.50:
A = 600
Therefore, there were 600 adults at the concert.