Question

Peter was in a line. There were twice as many students in front of him as behind him. Students (more than 3 but fewer than 9) left the line but Peter did not. Then twice as many students were behind Peter as in front. How many students left the line?

Answer 1

6 students

Step-by-step explanation:

x = the number of students in front of peter

y = the number of students behind peter

z = the number of students who left, for 3 < z < 9 ∴ z ∈ {4, 8}

system of equations:

• x = 2y

• 2(x-z) = y (assuming that the students who left were all among the students who are in front of peter)

x = 2y ⇒ y = x/2 (defining y with x)

2(x-z) = y (lets substitute y)

2(x-z) = x/2

2x-2z = x/2

2(2x-2z) = x

4x-4z = x

4x-x = 4z

3x = 4z

if z = 6 (i pluged the numbers from 4 to 8)

then

3x = 4×6

3x = 24

x = 24/3

x = 8

∴ y = 4

8 students were in front of peter and 4 were behind him

6 left

now 2 students are in front of peter and 4 are behind him

8 is twice 4

8-6 = 2

4 is twice 2

Answer 2

6 people left

Step-by-step explanation:

4 behind him 8 infront 6 left from infront leaving 4 behind 2 infront