Question 34418
Alright, so we want to write the "words" as "math".  

{{{.6x+g=x}}}
{{{.75x+g=x}}}
{{{.6x+(g-6)=.75x+g}}}
{{{.6x-.6x+(g-6)=.75x-.6x+g}}}
{{{g-6=.15x+g}}}
{{{100(g-6)=100(.15x+g)}}}
{{{100g-600=15x+100g}}}
{{{100g-600-100g=15x+100g-100g}}}
{{{-600=15x}}}
{{{-600/15=15x/15}}}
{{{-40=x}}}
See also,
*[invoke explain_simplification ".6x+(g-6)=.75x+g"]
Since there can't be a negative amount of people, we remove the negative sign getting:
{{{x=40}}}
Now we plug this into the original equation:
{{{.6(40)+g=40}}}
{{{24+g=40}}} So there are 24 boys in the class.
{{{24-24+g=40-24}}}
{{{g=16}}} There are 16 girls in the class.
So the answer is that on the first day of class there were 16 girls and 24 boys.

We can check that our answer works:
{{{.6*40=24}}} That works
{{{.4*40=16}}} That works
{{{16-6=10}}}
{{{24+6=30}}}
{{{.75*40=30}}} That works
{{{.25*40=10}}} That works
Yep, everything checks, we have the right answer.

Hope this helps,
lyra