There are two examination rooms, A and B. If 10 students are sent from A to B, then the number of students in each room is the same. If 20 candidates 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
Question
There are two examination rooms, A and B. If 10 students are sent from A to B, then the number of students in each room is the same. If 20 candidates 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
Solution
Let's denote the number of students in room A as a and the number of students in room B as b.
From the first condition, we know that if 10 students are sent from A to B, the number of students in each room is the same. This can be written as:
a - 10 = b + 10 => a = b + 20
From the second condition, we know that if 20 students are sent from B to A, the number of students in A is double the number of students in B. This can be written as:
a + 20 = 2 * (b - 20) => a = 2b - 40
Now we have a system of two equations, and we can solve it.
From a = b + 20 and a = 2b - 40, we get:
b + 20 = 2b - 40 => b = 60
Substitute b = 60 into the equation a = b + 20, we get:
a = 60 + 20 = 80
So, the number of students in room A is 80.
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