how to solve word problem

Question

there are two examination rooms A and B if 10students are sent from A to B then number of students in each room is the same. If 20 candidate are sent from B to A then the number of students in A is double the number of students in B the number of students in room A is

 

 

please explain in detail

Answer 1

if 10students are sent from A to B then number of students in each room is the same

 

If 10 are sent from A (A-10) to B (B+10) then the number of students is (=) the same

 

A-10 = B+10

 

If 20 candidate are sent from B (B-20) to A (A+20) then the number of students in A is double the number of students in B (2x)

 

A+20 = 2(B-20)

A+20 = 2B-40

 

Rearranging the first equation:

A=B+20

 

Then you can put this expression in for A in the second equation and solve for B

A+20 = 2B-40

(B+20)+20 = 2B-40

B+40 = 2B-40

B=80

Then plug this value back into the original equation to get the number of students in A:

A-10 = B+10

A-10 = 80+10

A=100