There are two consultation rooms named P and Q. If 10 patients are sent from P to Q, then the number of patients in each room is the same. If 20 patients are sent from Q to P, then the number of patients in P is double the number of patients in Q. The number of patients in room P is:
Question
There are two consultation rooms named P and Q. If 10 patients are sent from P to Q, then the number of patients in each room is the same. If 20 patients are sent from Q to P, then the number of patients in P is double the number of patients in Q. The number of patients in room P is:
Solution
Let's denote the number of patients in room P as x and the number of patients in room Q as y.
From the problem, we have two equations:
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x - 10 = y + 10 (This is because when 10 patients are sent from P to Q, the number of patients in each room is the same.)
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x + 20 = 2(y - 20) (This is because when 20 patients are sent from Q to P, the number of patients in P is double the number of patients in Q.)
Now, we can solve these two equations to find the values of x and y.
First, simplify equation 1) to get x = y + 20.
Then, substitute x = y + 20 into equation 2) to get y + 20 + 20 = 2(y - 20).
Simplify to get y + 40 = 2y - 40.
Finally, solve for y to get y = 80.
Substitute y = 80 into x = y + 20 to get x = 100.
So, the number of patients in room P is 100.
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