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Points A, B, C, and D are on the number line above [#permalink]
12 May 2016, 04:55
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Points A, B, C, and D are on the number line above, and AB = CD = \(\frac{1}{3}BC\) What is the coordinate of C ? A. \(\frac{13}{30}\) B. \(\frac{9}{20}\) C. \(\frac{11}{24}\) D. \(\frac{7}{15}\) E. \(\frac{29}{60}\) Practice Questions Question: 11 Page: 63
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Re: Points A, B, C, and D are on the number line above [#permalink]
12 May 2016, 05:05
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ExplanationFrom the figure you can see that since the coordinate of A is: \(\frac{1}{3}\), it follows that the coordinate of C is \(\frac{1}{3}+ AB + BC\). Since we are given that \(AB = \frac{1}{3}BC\) , the coordinate of C can be rewritten in terms of AB as follows: \(\frac{1}{3}+ AB + BC= \frac{1}{3} + AB + 3 AB = \frac{1}{3} + 4AB\) To find the coordinate of C, you need to know AB. From the figure, you know that AD = AB + BC + CD = AB + 3(AB) + AB = 5 (AB). On the other hand, since the coordinate of A is \(\frac{1}{3}\), and the coordinate of D is\(\frac{1}{2}\), it follows that \(AD = \frac{1}{2} \frac{1}{3}\) = \(\frac{1}{6}\). Therefore you can conclude that: \(\frac{1}{6}= 5 AB\) and \(AB= \frac{1}{30}\). Thus the coordinate of C is \(\frac{1}{3}+ 4AB = \frac{1}{3} + 4* \frac{1}{30}\) or \(\frac{7}{15}\). The correct answer is Choice D.
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Re: Points A, B, C, and D are on the number line above [#permalink]
15 Jul 2016, 05:34
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sandy wrote: Points A, B, C, and D are on the number line above, and AB = CD = \(\frac{1}{3}BC\) What is the coordinate of C ? A. \(\frac{13}{30}\) B. \(\frac{9}{20}\) C. \(\frac{11}{24}\) D. \(\frac{7}{15}\) E. \(\frac{29}{60}\) Distance from A to D = 1/2  1/3 = 3/6  2/6 = 1/6Let x = the distance from A to B This means that 3x = the distance from B to C And x = the distance from C to D So, the TOTAL DISTANCE from A to D = x + 3x + x = 5xSo, we can conclude that 5x = 1/6Divide both sides by 5 to get: x = 1/30 We want the coordinate of C. C is 1/30 LESS THAN 1/2 (the coordinate of D) 1/2  1/30 = 15/30  1/30 = 14/30 = 7/15 Answer:
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Re: Points A, B, C, and D are on the number line above [#permalink]
10 Feb 2017, 18:50
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How did you calculate that the distance from B to C was 3x?



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Re: Points A, B, C, and D are on the number line above [#permalink]
10 Feb 2017, 19:23
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EleV12 wrote: How did you calculate that the distance from B to C was 3x? AB = CD = (1/3)BC We can look at this in two equivalent ways: 1) AB is 1/3 the length of BC or 2) BC is 3 times the length of AB So, (if we use #2 above) if AB = x, then BC = 3x Cheers, Brent
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Re: Points A, B, C, and D are on the number line above [#permalink]
26 May 2017, 07:49
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each interval wll be ( 1/2  1/3 ) / 5 = 1/30 c is one interval behind d (1/2)
therfore c => 1/2  1/30 = 7/15



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Re: Points A, B, C, and D are on the number line above [#permalink]
31 May 2017, 14:08
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This is how I thought about it.
1. Instead of thinking of the point of A as 1/2 and the point of D as 1/3 think of them as points 0.5 and 0.33.
2. Since AB= 1/3 of BC that means that you can fit AB 3 times in BC, another way to think about it is AB=1/3 of BC, multiply both sides by 3 and get 3AB=BC. Also CD=AB.
3. You know that the distance between 0.5 and 0.33 is (0.50.33)= 0.17( this is the same as 1/21/3 =1/6 )
4. Up to this point you know 3 things.
a. The difference between points A and D is 0.17 (1/6) b. There are 5 equal parts from A to D ( which are AB+3 AB that you can fit in BC and CD that is equal to AB ) c. The C coordinate is on the 4th equal portion on the line. If you can figure out what is the value of each of the 5 portions then you just have to add this value 4 times ( one for each portion, to find the value for C).
5. To find the value for each of the 5 AB (portions) you just divide 0.17(total distance) by 5 (5 equal portions) and get 0.034 (which is the same as 1/6 divided 5= 1/30).
6. You now know that C is 1/30+1/30+1/30+1/30 from A and A is 1/3 so if you add all up will get 1/3+4(1/30) which is 7/15. (The previous is the same as 0.33+4(0.034) which is 0.466




Re: Points A, B, C, and D are on the number line above
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31 May 2017, 14:08





