A theater that is rectangular in shape seats 720 people.The number of rows needed to seat the people would be 4 less if each row held 6 more people.How many people would then be in each row?
If there are now x rows, then each row has 720/x seats.
The new configuration means that
(x-4)(720/x + 6) = 720
(x-4)(6x+720) = 720x
(x-4)(x+120) = 120x
x^2-4x-480 = 0
(x+20)(x-24) = 0
...
To find out how many people would be in each row, we can set up an equation based on the given information.
Let's assume that the original number of rows is represented by 'x'. In that case, the number of seats in each row would be '720 / x'.
According to the problem, if each row held 6 more people, the number of rows would be 4 less. This means the new number of rows would be 'x - 4' and the number of seats in each row would be '720 / (x - 4)'.
Since the number of seats in each row would be 6 more in the second case, we can set up an equation:
720 / x = (720 / (x - 4)) + 6
To solve this equation, we can cross-multiply and simplify:
720(x - 4) = 720x + 6(x - 4)
720x - 2880 = 720x + 6x - 24
720x - 720x - 6x = 24 - 2880
-6x = -2856
Dividing both sides of the equation by -6, we find:
x = 476
Therefore, the original number of rows required to seat 720 people is 476.
To find out how many people would be in each row, we can substitute this value back into the equation of the original number of seats in each row:
720 / 476
Simplified, the answer is approximately 1.51, or rounded to the nearest whole number, there would be 2 people in each row.