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# Point A, B , C and D lies on a straight line

+1
2184
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Point A, B , C and D lies on a straight line

AB : BD = 1:5

AC : CD = 7:11

Work out AB : BC : CD

thanks

Nov 22, 2017

#2
+7354
+3

This is a neat question!!

This drawing shows the information from the problem:

1s + 5s   =   7t + 11t

6s   =   18t

1s   =   3t               (This is like a unit conversion!)

And...

AB : BC : CD

=  1s : 7t - 1s : 11t                  Let's "convert"  s  into  t ,  using  1s  =  3t .

=  3t : 7t - 3t : 11t

=  3t : 4t : 11t

=  3 : 4 : 11

Nov 22, 2017
edited by hectictar  Nov 22, 2017
edited by hectictar  Nov 22, 2017

#1
+99539
+3

Haven't seen one like this before.....!!!

Since AB : BD  =  1 : 5   so...from A to D  there are  1 + 5 = 6 parts

And since AC : CD  = 7 : 11   and we can divide each 6th part into 7 + 11 = 18 more parts

So.....from A to D there are   6 * 18  =   108  equal parts

So  AB  =   [108 / 6] * 1  = 18  units

And BD  =  [108 / 6] * 5  = 90 units

And AC =  [ 108/ 18] * 7  = 42 units

And CD  =  [ 108 / 18] * 11 =   66 units

AB  = 18

BC =  AC - AB =  42 - 18  =  24 units

CD  =  66 units

A           B            C                D

18    +    24     +        66            =       108

So   AB :   BC : CD    =    18 : 24 : 66  =    3 : 4 : 11

Nov 22, 2017
#2
+7354
+3

This is a neat question!!

This drawing shows the information from the problem:

1s + 5s   =   7t + 11t

6s   =   18t

1s   =   3t               (This is like a unit conversion!)

And...

AB : BC : CD

=  1s : 7t - 1s : 11t                  Let's "convert"  s  into  t ,  using  1s  =  3t .

=  3t : 7t - 3t : 11t

=  3t : 4t : 11t

=  3 : 4 : 11

hectictar Nov 22, 2017
edited by hectictar  Nov 22, 2017
edited by hectictar  Nov 22, 2017
#3
+99539
+2

Thanks, hectictar......I was "feeling my way," here....but...I like your method better  !!

Nov 22, 2017
#4
+7354
+3

Thank you! I think I learned something new from this problem!

Nov 22, 2017