SOLUTION: P, Q, R, S, and T are on line k such that Q is the midpoint of segment PT, R is the midpoint of segment QT, and S is the midpoint of segment RT. If segment PS = 9, then what is PT?

Question 1090433: P, Q, R, S, and T are on line k such that Q is the midpoint of segment PT, R is the midpoint of segment QT, and S is the midpoint of segment RT. If segment PS = 9, then what is PT?
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
Q is the midpoint of PT,
so PQ=QT.
R is the midpoint of QT,
so QR=RT.
S is the midpoint off RT,
so RS=ST.
Let us say RS=ST=x .
Then, RT=RS+ST=x+x=2x ,
so RT=QR=2x .
Then, QT=QR+RT=2x+2x=4x ,
and PQ=QT=4x .
Then, PS=PQ+QR+RS=4x+2x+x=7x ,
and PT=PQ+QT=4x+4x=8x .
The problem says that PS=9 ,
so , ,
and PT=8x= .

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