Question

When a group of students are seated 3 to a bench in an auditorium, 18 are left standing. If they were seated 4 to a bench, 3 benches would be empty. Find the number of benches and students

Answer 1

• Total number of benches= 30

• Total number of students= 108

Explanation:

let the total number of benches in the auditorium be x.

Now if in each bench 3 students are to be seated.

Then 18 students are left standing.

This means that the number of students in total are: 3x+18

Also, if 4 students are to be seated in a bench then three benches are left empty.

This means that the total number of students are:

4(x-3)

Hence, the two quantities are equal.

i.e.

`3x+18=4(x-3)\\\\i.e.\\\\3x+18=4x-12\\\\i.e.\\\\4x-3x=18+12\\\\i.e.\\\\x=30`

Also, when x=30

then,

`3x+18=3* 30+18\\\\i.e.\\\\3x+18=108`

Hence, total number of benches=30

and Total number of students=108

Answer 2

x = students

b = benches

when 3 are on a bench and 18 are standing the equation is:

x = 3b+18

when 4 are sitting and 3 benches are empty the formula is

and x = 4b-12

so 3b+18 = 4b-12

rearrange to

4b-3b = 18 +12

so b = 30

now plug that into the first formula

x=3(30)+18 = 108

so 108 students and 30 benches