Question 40785
Let's call X to the original number of boys and Y to the number of girls. If 60% of the students are boys, this means that:

{{{X/(X+Y) = 0.6}}}

{{{X = 0.6(X+Y)}}}
{{{X = 0.6X + 0.6Y}}}
{{{0.4X = 0.6Y}}}
{{{X = (3/2)Y}}}

Now, if we have 6 more boys and 6 less girls, the percentage of boys grows to 75%. So we get that:

{{{ (X + 6)/(X+6+Y-6) = 0.75}}}
{{{ (X+6)/(X+Y) = 0.75}}}
{{{X+6 = 0.75X + 0.75Y}}}

And now we simply plug {{{X=(3/2)Y}}} into this equation:

{{{(3/2)Y + 6 = 0.75*(3/2)Y + 0.75Y}}}
{{{6 = 0.375Y}}}
{{{Y = 16}}}


{{{X = (3/2)16 = 24}}}

So originally there were 16 girls and 24 boys.


I hope this helps!
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