<PRE><B>Question 1101317</B>
at a fair ghe ratio of boys to girls is 4:7.
after one third of the boys and one quarter of the girls left, 570 children were left.
how many were at the fair at the start?
:
let x = the multiplier
then
4x = no. of boys
and
7x = no. of girls
:
2/3 of the boys and 3/4 of the girls stayed 
{{{2/3}}}4x + {{{3/4}}}7x = 570
multiply by 12 to clear the denominators
8(4x) + 9(7x) = 12(570)
32x + 63x = 6840
95x = 6840
x = {{{6840/95}}}
x = 72 is the multiplier
therefore originally:
4(72) = 288 boys
7(72) = 504 girls
-------------------
totals: 792 kids at the start
:
;
Check this
{{{2/3}}}(288) + {{{3/4}}}504 = 
192 + 378 = 570
</PRE>