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

Question

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Answer 1

If three pieces of string have lengths in the ratio 5:6:1 then the lengths of those strings can be represented by 5x, 6x , and x where x is the "constant of proportionality. You can use any letter you want, for example:

5k,6k,k.

So the lengths of the string could be 5,6,1 or 10,12,2, or 20, 24,4 (infinite number of possibilities. And k does not have to be an integer.

The point is that for this problem the segment lengths can also be represented by 5x,6x and x. But we know the entire length is 36 because OP+PQ+QR = 36 (segment addition postulate.

So, 5x+6x+x = 36. Solve for x, then pay attention to what the question is asking for : OQ = OP+PQ.