The general admission costs $2.00
The reserved seats cost $6.00
The total collected from admissions was: $3104.00
and 984 people paid for admissions.
We are asked to find how many general and how many reserved admissions were sold.
Since these are our unknowns, we give to them letters:
g = Number of general admissions sold
r = number of reserved seats admissions sold
We can now create two different equations:
The first one concerning the total numer of admission which should includenthe addition of the genaral admissions (g) and the reserved seats (r):
Equation 1 ) g + r = 984
The nex equation will be associated with the amount in dollars coming fro selling g of the general admissions at $2 each (2 * g), and also the amount in dollars coming from selling "r" reserved seats at $6 each (6 * r):
Equation 2) 2 g + 6 r = 3104
To solve this system of equations, we solve for one of the unknows (for example for "g") in equation 1):
g = 984 - r
We call this our "substitution equation" since irt allows us to substitute the g with an expression that contains 'r"
We use it in equation 2)
2 g + 6 r = 3104
2 (984 - r) + 6 r = 3104
and now we solve for r in the equation:
1968 - 2 r + 6 r = 3104
4 r = 3104 - 1968
4 r = 1136
r = 1136/4
r = 284 (this is the number of reserved seats that were sold)
Now, we can find what number of general admissions sold by replacing r with 284 in the "substitution equation":
g = 984 - r
g = 984 - 284
g = 700
So there were:
700 general admissions sold, and 284 reserved seats sold.oe