Question

50 points

There are some benches in a classroom. If 4 Students sit on each bench three branches are left vacant and if 3 students sit on each bench Three Students are left standing. What is the total number of students in the class?​

Answer 1

Let the number of students =

y

let the number of benches =

x

from the first statement

y

=

4

x

−

12

(three empty benches * 4 students)

from the second statement

y

=

3

x

+

3

Substituting equation 2 into equation 1

3

x

+

3

=

4

x

−

12

rearranging

x

=

15

Substituting the value for x in equation 2

y

=

3

⋅

15

+

3

=

48

Answer 2

Hi buddy

Here is your answer

Let the number of students = y

let the number of benches = x....

from the first statemen y =

4

4x

4x−

4x−12

4x−12 (three empty benches * 4 students)

4x−12 (three empty benches * 4 students)from the second statement

4x−12 (three empty benches * 4 students)from the second statementy

4x−12 (three empty benches * 4 students)from the second statementy=

4x−12 (three empty benches * 4 students)from the second statementy=3

4x−12 (three empty benches * 4 students)from the second statementy=3x

4x−12 (three empty benches * 4 students)from the second statementy=3x+

4x−12 (three empty benches * 4 students)from the second statementy=3x+3

4x−12 (three empty benches * 4 students)from the second statementy=3x+3

4x−12 (three empty benches * 4 students)from the second statementy=3x+3 Substituting equation 2 into equation 1

4x−12 (three empty benches * 4 students)from the second statementy=3x+3 Substituting equation 2 into equation 13

4x−12 (three empty benches * 4 students)from the second statementy=3x+3 Substituting equation 2 into equation 13x

4x−12 (three empty benches * 4 students)from the second statementy=3x+3 Substituting equation 2 into equation 13x+

4x−12 (three empty benches * 4 students)from the second statementy=3x+3 Substituting equation 2 into equation 13x+3

4x−12 (three empty benches * 4 students)from the second statementy=3x+3 Substituting equation 2 into equation 13x+3=

4x−12 (three empty benches * 4 students)from the second statementy=3x+3 Substituting equation 2 into equation 13x+3=4

4x−12 (three empty benches * 4 students)from the second statementy=3x+3 Substituting equation 2 into equation 13x+3=4x

4x−12 (three empty benches * 4 students)from the second statementy=3x+3 Substituting equation 2 into equation 13x+3=4x−

4x−12 (three empty benches * 4 students)from the second statementy=3x+3 Substituting equation 2 into equation 13x+3=4x−12

4x−12 (three empty benches * 4 students)from the second statementy=3x+3 Substituting equation 2 into equation 13x+3=4x−12

4x−12 (three empty benches * 4 students)from the second statementy=3x+3 Substituting equation 2 into equation 13x+3=4x−12 x

4x−12 (three empty benches * 4 students)from the second statementy=3x+3 Substituting equation 2 into equation 13x+3=4x−12 x=

4x−12 (three empty benches * 4 students)from the second statementy=3x+3 Substituting equation 2 into equation 13x+3=4x−12 x=15

4x−12 (three empty benches * 4 students)from the second statementy=3x+3 Substituting equation 2 into equation 13x+3=4x−12 x=15

4x−12 (three empty benches * 4 students)from the second statementy=3x+3 Substituting equation 2 into equation 13x+3=4x−12 x=15 Substituting the value for x in equation 2

4x−12 (three empty benches * 4 students)from the second statementy=3x+3 Substituting equation 2 into equation 13x+3=4x−12 x=15 Substituting the value for x in equation 2y

4x−12 (three empty benches * 4 students)from the second statementy=3x+3 Substituting equation 2 into equation 13x+3=4x−12 x=15 Substituting the value for x in equation 2y=

4x−12 (three empty benches * 4 students)from the second statementy=3x+3 Substituting equation 2 into equation 13x+3=4x−12 x=15 Substituting the value for x in equation 2y=3

4x−12 (three empty benches * 4 students)from the second statementy=3x+3 Substituting equation 2 into equation 13x+3=4x−12 x=15 Substituting the value for x in equation 2y=3⋅

4x−12 (three empty benches * 4 students)from the second statementy=3x+3 Substituting equation 2 into equation 13x+3=4x−12 x=15 Substituting the value for x in equation 2y=3⋅15

4x−12 (three empty benches * 4 students)from the second statementy=3x+3 Substituting equation 2 into equation 13x+3=4x−12 x=15 Substituting the value for x in equation 2y=3⋅15+

4x−12 (three empty benches * 4 students)from the second statementy=3x+3 Substituting equation 2 into equation 13x+3=4x−12 x=15 Substituting the value for x in equation 2y=3⋅15+3

4x−12 (three empty benches * 4 students)from the second statementy=3x+3 Substituting equation 2 into equation 13x+3=4x−12 x=15 Substituting the value for x in equation 2y=3⋅15+3=

4x−12 (three empty benches * 4 students)from the second statementy=3x+3 Substituting equation 2 into equation 13x+3=4x−12 x=15 Substituting the value for x in equation 2y=3⋅15+3=48

Hope it help you

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