Answer:
To solve the given problem using elimination and substitution, we can set up a system of equations based on the information provided. Let's denote the number of adult tickets sold as "a" and the number of student tickets sold as "s".
From the given information, we can establish two equations:
1. The total number of tickets sold is 498:
a + s = 498
2. The total revenue from ticket sales is $8,100:
18.75a + 7.50s = 8100
Now, we can solve this system of equations using either elimination or substitution.
Method 1: Elimination
To eliminate one variable, we can multiply the first equation by -7.50 and the second equation by 1 to make the coefficients of "s" equal and opposite:
-7.50(a + s) = -7.50(498)
18.75a + 7.50s = 8100
This simplifies to:
-7.50a - 7.50s = -3735
18.75a + 7.50s = 8100
Adding these two equations eliminates "s":
11.25a = 4365
Dividing both sides by 11.25 gives us:
a = 388
Therefore, there were 388 adult tickets sold.
Method 2: Substitution
We can solve the first equation for "s" in terms of "a":
s = 498 - a
Substituting this value into the second equation:
18.75a + 7.50(498 - a) = 8100
Expanding and simplifying:
18.75a + 3735 - 7.50a = 8100
11.25a = 4365
Dividing both sides by 11.25 gives us:
a = 388
Again, we find that there were 388 adult tickets sold.
Therefore, using either elimination or substitution, we determine that 388 adult tickets were sold for the Broadway show.
Explanation: