We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.

+0

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

+1
2680
4
+846

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

### Best Answer

#2
+8439
+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

### 4+0 Answers

#1
+101872
+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
+8439
+3
Best Answer

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
+101872
+2

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

Nov 22, 2017
#4
+8439
+3

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

Nov 22, 2017