There are two classrooms A and B containing students. If 5 students are shifted from room A to room B, the resulting number of students in the two rooms become equal. If 5 students are shifted from room B to room A, the resulting number of students in room A becomes double the number of students left in room B. Find the original number of students in the rooms.
Answers
Answer:
Class room A = 35, Class room B = 25
Step-by-step explanation:
Let the number of students in class A = x
Let the number of students in class B = y
Case 1: When 5 students are transferred from class A to class B
Number of students in class A = x-5
Number of students in class B = y+5
Given that;
Number of students in class A = Number of students in class B
=>x-5 = y+5
x-y-5-5 = 0
x-y-10 = 0 ……… eq(1)
Case 2: When 5 students are transferred from class B to class A
Number of students in class A = x+5
Number of students in class B = y-5
Given that;
Number of students in class A = 2 * (Number of students in class B)
x+5 = 2 * (y-5)
x+5 = 2y - 10
x-2y+5+10 = 0
x-2y+15 = 0 ……… eq(2)
Solving equations (1) & (2)
x - y - 10 = 0
x - 2y +15 = 0
(-). (+) (-)
————————
y - 25 = 0
=> y = 25
From equation(1);
x-y-10 = 0
x-25-10 = 0
x-35 = 0
x = 35
Therefore, the original number of students in the class rooms are;
In Class A = x = 35
In Class B = y = 25
Answer:
35 students in Class A
25 Students in Class B
Step-by-step explanation:
There are two classrooms A and B containing students. If 5 students are shifted from room A to room B, the resulting number of students in the two rooms become equal. If 5 students are shifted from room B to room A, the resulting number of students in room A becomes double the number of students left in room B. Find the original number of students in the rooms.
Let say students in classrooms A = A
Let say students in classrooms B = B
A - 5 = B + 5
=> A = B + 10 - eq 1
A + 5 = 2(B-5)
=> A + 5 = 2B - 10
=> A = 2B - 15 - eq 2
Equating Both
B + 10 = 2B - 15
=> B = 25
A + 25 + 10 = 35
A = 35
35 students in Class A
25 Students in Class B