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Points Q and R are on segment PS, which has length 24. If PQ is half as long as QS, and QR is 3 times as long as RS, how long is RS?

 

 Dec 2, 2019
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First, we know that segment PS is 24 units long. We will want to find QS in order to find RS. So, let's find QS

 

We know that PQ is half as long as QS, meaning 2 PQ = QS

 

We can take this as PQ + QS = PS -> PQ + 2PQ = PS -> 3PQ = PS

 

PS is 24 units.

 

3PQ=24

 

Divide by 3.

 

PQ=8

 

Finding PQ, we can now figure out the answer for 2PQ = QS.

 

2(8)=QS

 

16=QS

 

QS is 16 units long. 

 

In order to find RS, we need to create a similar equation as finding QS

 

QS= RS + QR

QR=3RS

 

Substitute 3RS for QR in the first equation. Substitute 16 for QS in the first equation

 

16 = RS + 3RS

16 = 4RS

RS = 4

 

So, we now know that RS is 4 units long.

 Dec 2, 2019

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