A new auditorium is being built for a college. The balcony has 60 seats. Thefloor has 15 rows with x seats in each row. The number of people in theauditorium must be under 315 to meet safety regulations.What is the solution of this inequality, and what is its meaning?

Respuesta :

x < 17

This means the new auditorium must have less than 17 seats 1n each row on the floor to meet the safety regulations.

Explanation:

Number seats in the balcony = 60

Number of seats on the floor = number of rows × number of seats on each row

Number of seats on the floor = 15× x = 15x

The number of people in the auditorium must be under 315:

This means the number of people can be less than 315 but not above it.

We represent less than 315 as < 315

The inequality equation:

Number seats in the balcony + Number of seats on the floor < 315

60 + 15x < 315

Rewritting the inequality equation:

15x + 60 < 315

Solving the inequality:

15x + 60 < 315

collect like terms by subtracting 60 from both sides:

15x + 60 - 60 < 315 -60

15x < 255

Divide both sides by 15:

15x/15 < 255/15

x < 17

This means the new auditorium must have less than 17 seats in each row on the floor to meet the safety regulations.