SOLUTION: One apartment is directly above a second apartment. A resident living downstairs calls his neighbor living above him and states" If one of you is willing to come downstairs we'll h

Question 399991: One apartment is directly above a second apartment. A resident living downstairs calls his neighbor living above him and states" If one of you is willing to come downstairs we'll have the same number of people in both apartments." The upstairs resident responds,"We're all too tired to move. Why don't one of you come up here? Then we will have twice as many people up here as you've got down there." How many people are in each apartment?
A + 1 =B(2) A +1 = 2B
B + 1 =A B + 1 =A B= A- 1 substitute: A + 1 = 2(A-1) resulting in A + 1 = 2A -2
-A + 2 = -A -2
3=A
doesn't result in correct answer....
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
One apartment is directly above a second apartment. A resident living downstairs calls his neighbor living above him and states" If one of you is willing to come downstairs we'll have the same number of people in both apartments." The upstairs resident responds,"We're all too tired to move. Why don't one of you come up here? Then we will have twice as many people up here as you've got down there." How many people are in each apartment?
------------
Initial numbers.
Let x people be upstairs
Let y people be downstairs
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1st proposal equation:
y+1 = x-1
---
2nd proposal equaltion:
x+1 = 2(y-1)
===================
Solve the system:
y = x-2
Substitute to get:
x+1 = 2(x-2-1)
x+1 = 2x-6
x = 7 (number of people upstairs initially)
---
Solve for "y":
y = x-2
y = 7-2
y = 5 (number of people downstairs initially)
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Cheers,
Stan H.
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