The points G, H, I and J all lie on the same line segment, in that order, such that the ratio of G, H, colon,

Question

The points G, H, I and J all lie on the same line segment, in that order, such that the ratio of G, H, colon, H, I, colon, I, JGH:HI:IJ is equal to 3, colon, 3, colon, 2, .3:3:2. If G, J, equals, 24, commaGJ=24, find H, J, .HJ.

GPT-5 mini · Answer

Let the common factor be k. Then GH = 3k, HI = 3k, IJ = 2k, so GJ = 3k+3k+2k = 8k = 24 → k = 3.  
HJ = HI + IJ = 3k + 2k = 5k = 5·3 = 15.

The points G, H, I and J all lie on the same line segment, in that order, such that the ratio of G, H, colon, H, I, colon, I, JGH:HI:IJ is equal to 3, colon, 3, colon, 2, .3:3:2. If G, J, equals, 24, commaGJ=24, find H, J, .HJ.

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