Question:
A new auditorium is being built for a college. The balcony has 200 seats. The floor has 25 rows with x seats in each row. The number of people in the auditorium must be under 750 to meet safety regulations. What is the solution of this inequality, and what is its meaning?
Answer:
[tex]200 + 25x < 750[/tex]
Number of seats in a row must be less than 22
Step-by-step explanation:
Given
Total = Less than 750
Current Seats = 200
Rows = 25
Seat per row = x
Required
Represent as an inequality
The scenario will be represented as:
[tex]Current\ Seats + Rows * x = Total[/tex]
Substitute 200 for Current Seats
[tex]200 + Rows * x = Total[/tex]
Substitute 25 for Rows
[tex]200 + 25* x = Total[/tex]
[tex]200 + 25x = Total[/tex]
Substitute <750 for Total.
The equation then becomes
[tex]200 + 25x < 750[/tex]
Solving further:
[tex]25x < 750 - 200[/tex]
[tex]25x < 550[/tex]
[tex]x < \frac{550}{25}[/tex]
[tex]x < 22[/tex]
This means that:
Number of seats in a row must be less than 22
