Answer
There are 5 people in downstairs and 7 people above.
Work Step by Step
Let x people are in downstairs and y in the above apartment respectively.
The statements form linear equations. Form equation by bit-by-bit of the statements.
Statement 1:
“If one of you is willing to come downstairs.”This implies that \[\left( x+1 \right)\].
“We’llhave the same number of people in both apartments”.
Hence,
\[\left( x+1 \right)=\left( y-1 \right)\](I)
Statement 2:
“Why don’t one of you come up here? This implies,\[\left( y+1 \right)\].
Then, we will have twice as many people up here as you’ve got down there”
Hence,
\[\left( y+1 \right)=2\left( x-1 \right)\](II)
Rearranging the terms in equation (I),
\[y=x+2\](III)
Substitute equation (III) in equation (II),
\[\begin{align}
& \left( x+2+1 \right)=2\left( x-1 \right) \\
& x+3=2x-2 \\
& x=5
\end{align}\]
Substitute x value in equation (III),
\[y=7\]
Hence, there are 5 people in downstairs and 7 people above.
