word problems

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 initially was

Answer 1

Let A and B = the initial number of students in rooms A and B respectively.

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

A-10 = B + 10
So, A = B + 20

• If 20 candidates are sent from B to A then the number of students in A is double the number of students in B:

(A-10)+20 = 2*(B+10-20)
A+10 = 2*(B-10)

 

Since A = B+20, let's substitute B+20 in place of A in the second equation:

A+10 = 2*(B-10)

(B+20) + 10 = 2B - 20

B + 30 = 2B -20

50 = B

 

Now find A:

A = B + 20

A = 50 + 20

A = 70

 

Check:

A-10 = B + 10

70-10 = 50+10

60 = 60

 

A+10 = 2*(B-10)

70+10 = 2(50-10)

80 = 2(40)

80 = 80

 

Check!