An auditorium seats 1500 people. Floor seats cost $15 and balcony seats cost $10. If the place is sold out and they make $2100 how many seats are on the floor and in the balcony?
number on the floor --- g
number on balconey --- b
g + b = 1500
15f + 10b = 2100 ---> 3f + 2b = 420
solve for g and b
hint: double the first and subtract from the 2nd
To determine the number of seats on the floor and in the balcony, we can set up a system of equations based on the given information.
Let's assume that the number of floor seats is represented by 'F', and the number of balcony seats is represented by 'B'.
According to the problem, the total number of seats in the auditorium is 1500. Therefore, we can write our first equation as:
F + B = 1500
Additionally, we are provided with the cost of each seat. The floor seats cost $15, and the balcony seats cost $10. The total revenue from all the sold-out seats is $2100. We can represent this as our second equation:
15F + 10B = 2100
Now, we can solve these equations simultaneously to find the values of 'F' and 'B'.
First, let's solve equation 1 for 'F':
F = 1500 - B
Now substitute this value of 'F' into the second equation:
15(1500 - B) + 10B = 2100
Simplifying the equation:
22500 - 15B + 10B = 2100
22500 - 5B = 2100
-5B = 2100 - 22500
-5B = -20400
B = -20400/-5
B = 4080
Now substitute the value of 'B' back into equation 1 to find 'F':
F = 1500 - 4080
F = 1500 - 4080
F = 10920
However, this solution implies that there are negative seats, which is not possible. Therefore, it seems there was an error in the problem statement. Please recheck the values provided or the problem statement to get a valid solution.