Question 1168562
A, B, C, D, and E. are consecutive points on a line. If AB/BC=1/3, BC/CD=1/4,
and CD/DE=1/2, what is AC/BE ?
<pre>

Begin by letting AB = 1 unit.  Then you'll see how I got these numbers:

{{{drawing(800,400,-1,41,-2,2,line(0,0,40.3,0),
circle(.25,0,.15),
circle(1.25,0,.15),
circle(4.2,0,.15),
circle(16.2,0,.15),
circle(40.2,0,.15),
locate(.5,.2,1),locate(2.5,.2,3),locate(10,.2,12),locate(28,.2,24),


locate(0,-.03,A), 


locate(1,-.03,B),locate(4,-.03,C),locate(16,-.03,D),locate(40,-.03,E))}}}

let AB = 1 unit, then

{{{(AB)/(BC)=1/3}}}
{{{1/(BC)=1/3}}}
Cross-multiply,
{{{3=BC}}}
So BC = 3 units

{{{(BC)/(CD)=1/4}}}
{{{3/(CD)=1/4}}}
Cross-multiply,
{{{12=CD}}}
So CD = 12 units

{{{(CD)/(DE)=1/2}}}
{{{12/(DE)=1/2}}}
Cross-multiply,
{{{24=DE}}}
So DE = 24 units

</pre>what is AC/BE ?<pre>

AC = AB+BC = 1+3 = 4
BE = BC+CD+DE = 3+12+24 = 39

So

{{{(AC)/(BE) = 4/39}}}

Edwin</pre>