Question

An auditorium has rows of seats with a seats in each row Kayla

knows there are at least 70 seats but fewer than 156 seats in the
auditorium. How many rows of seats can there be in the auditorium
Use Exercises 1-a to answer the question
1. Explain how you would find the least possible number of rowe
in the auditorium
2. How would you find all the possible numbers of rows, without
having to check if & is a factor of every number between
70 and 1507
3. Name all the possible numbers of rows in the auditorium,

Answer 1

1. 9 rows

2. see below

3. 9, 10, 11, 12, 13, 14, 15, 16, 17, 18

Explanation:

Please note that I believe there are typing errors in the question and that the given information should be:

• 8 seats in each row
• At least 70 seats
• Less than 150 seats

Question 1

To determine the least possible number of rows in the auditorium, divide the least number of seats by the number of seats in a row:

⇒ 70 ÷ 8 = 8.75

As the answer is a decimal, round it up to the nearest whole number.

Therefore, the least possible number of rows in the auditorium is 9 rows.

Question 2

Find the greatest number of rows by dividing the greatest number of seats by the number of seats in a row:

⇒ 150 ÷ 8 = 18.75

As there should be fewer than 150 seats we cannot round the number up (as this would make there be more than 150 seats), so instead must round it down to 18.

Therefore, the greatest number of rows in the auditorium is 18 rows.

Question 3

As we have found the least number of rows in question 1 and the greatest number of rows in question 2, all we need to do is list all the numbers between (and including) these numbers.

Therefore, all the possible numbers of rows in the auditorium are:

9, 10, 11, 12, 13, 14, 15, 16, 17, 18

Answer 2

Explanation:

• Note: there is a typo, 'a' should be '8'

The number of seats in each row is 8 and the total number of seats is between 70 and 150.

Let x be the number of rows, then we have the inequality:

• 70 ≤ 8x < 156

Divide all sides by 8 to get:

• 70/8 ≤ x < 156/8
• 9 ≤ x ≤ 19 (taking closest integers)

So the number of rows is between 9 and 19 both inclusive.

All possible number of rows

• 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19