a band held a concert in it's hometown a total of 15000 people attended the tickets cost 8.50 per student and 12.50 per adult the concert took in a total of $162500 how many adult came to the concert
12.5A+8.5S=162500
A+S=15000
To find the number of adults who came to the concert, we need to set up an equation based on the given information.
Let's say the number of students who attended the concert is S, and the number of adults who attended is A.
According to the problem, the total number of people who attended the concert is 15000. So, we have the equation:
S + A = 15000 (equation 1)
The cost of a student ticket is $8.50, and the cost of an adult ticket is $12.50.
The total revenue from ticket sales is given as $162,500. We can use this information to set up another equation:
8.50S + 12.50A = 162,500 (equation 2)
Now, we have a system of two equations to solve:
S + A = 15000
8.50S + 12.50A = 162,500
We can solve this system of equations using substitution or elimination method.
Let's solve it using the elimination method. Multiply equation 1 by 8.50 to make the coefficients of S in both equations the same:
8.50S + 8.50A = 127,500 (equation 3)
Now, subtract equation 3 from equation 2:
8.50S + 12.50A - (8.50S + 8.50A) = 162,500 - 127,500
This simplifies to:
4A = 35,000
Divide both sides by 4:
A = 8,750
Therefore, the number of adults who attended the concert is 8,750.