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The points O, P, Q and R all lie on the same line segment, in that order, such that the ratio of OP: PQ : QR is equal to 5:6: 1. If OR = 36, find OQ.

1 Answer

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The Ratio OP: PQ: QR = 5: 6: 1 means that if the line segment OR is 5 + 6 + 1 = 12 then


(OP)/(OR)=(5)/(12)
(PQ)/(OR)=(6)/(12)
(QR)/(OR)=(1)/(12)

But, the problem is that OR is not 12, rather, it is 36; therefore, we need to multiply the ratios above by 36:


\begin{gathered} (OP)/(OR)=(5)/(12)\rightarrow OP=(5)/(12)OR \\ \end{gathered}
OP=(5)/(12)*36
OP=15
(PQ)/(OR)=(6)/(12)\rightarrow PQ=(6)/(12)* OR
PQ=(6)/(12)*36
PQ=18
(QR)/(OR)=(1)/(12)\rightarrow QR=(1)/(12)* OR
QR=(1)/(12)*36
QR=3

Hence, we have the lengths OP, PQ, and QR.

The line segment OQ is


OQ=OP+PQ

therefore,


OQ=15+18
OQ=33.

which is our answer!

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