<PRE><B>Question 1129109</B>
let m = time required by 1 man to complete the job
let w = time required by 1 woman
let c = time required by 1 child
let the completed job = 1
:
3 men and 5 women do a piece of work in 9 days
{{{9/(3m)}}} + {{{9/(5w)}}} = 1
 and 2 men and 7 children do the same in 6 days.
{{{6/(2m)}}} + {{{6/(7c)}}} = 1
reduce the fractions
{{{3/m}}} + {{{9/(5w)}}} = 1
{{{3/m}}} + {{{6/(7c)}}} = 1
we have 3/m in both equations, therefore
{{{9/(5w)}}} = {{{6/(7c)}}}
cross multiply
9(7c) = 6(5w)
63c = 30w
divide both sides by 3
21c = 10w
:
 how many women can do as much work as 21 children ? 
From the above equation we can see 10 women can do the work of 21 children</PRE>