Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 2.0 Junior Find the answer

If points $P, Q, R$ , and $S$ are arranged in order on a line segment with $P Q=1, Q R=2 P Q$ , and $R S=3 Q R$ , what is the length of $P S$ ?

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

Since $P Q=1$ and $Q R=2 P Q$ , then $Q R=2$ . Since $Q R=2$ and $R S=3 Q R$ , then $R S=3(2)=6$ . Therefore, $P S=P Q+Q R+R S=1+2+6=9$ .

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