<PRE><B>Question 286029</B>
A group containing boys and girls took a test. 
If exactly 2/3 of the boys and exactly 3/4 of the girls passed the test,
 and if an equal number of boys and girls passed the test, 
then what fraction of the entire group passed the test? 
:
b = total no. of boys
g = total no. of girls
(b+g) = total in group
:
{{{2/3}}}b = {{{3/4}}}g
multiply both sides by 12
4(2)b = 3(3)g
8b = 9g
{{{b/g}}} = {{{9/8}}}
Equal boy and girls passed so we can say:
{{{2/3}}}9 = {{{3/4}}}8
6 = 6; therefore 12 represent total that passed
9 + 8 = 17 represents total students
:
{{{12/17}}} fraction that passed</PRE>