for a given performance, 4 1/4 times as many tickets were sold as there were seats. If 5100 tickets were sold, how many could be seated in the auditorium?
4 1/4 = 4.25
4.25x = 5100
x = 1,200
Step 1: Let's assume the number of seats in the auditorium as "x".
Step 2: According to the problem, 4 1/4 times as many tickets were sold as there were seats. This can be written as 4 1/4 * x.
Step 3: The problem states that 5100 tickets were sold. So, we can write it as 4 1/4 * x = 5100.
Step 4: To solve this equation, we need to convert the mixed fraction to an improper fraction, and also convert the mixed number into a proper fraction. 4 1/4 can be written as 17/4.
So, the equation becomes (17/4)*x = 5100.
Step 5: Multiply both sides of the equation by the reciprocal of 17/4, which is 4/17.
(x) = (5100)*(4/17).
Step 6: Simplifying the equation further, x = 1200.
Thus, the auditorium can seat 1200 people.
To find the number of seats in the auditorium, we can use the equation:
Number of tickets sold = Number of seats × (4 1/4)
Given that 5100 tickets were sold, we can substitute this value into the equation:
5100 = Number of seats × (4 1/4)
We need to convert the mixed number, 4 1/4, to an improper fraction. To do this, multiply the whole number (4) by the denominator (4), and then add the numerator (1). The result will be the new numerator:
4 × 4 + 1 = 17
The denominator remains the same (4). So, 4 1/4 can also be represented as the improper fraction 17/4.
Now, let's substitute this fraction into the previous equation:
5100 = Number of seats × (17/4)
To isolate the number of seats, we need to divide both sides of the equation by (17/4). This is equivalent to multiplying by the reciprocal (4/17):
Number of seats = 5100 × (4/17)
Now, let's calculate this:
Number of seats = 1200
Therefore, there could be 1200 seats in the auditorium.