Question 930255
When 1/5 of the boys left, there were still b boys and g girls who stayed to see
the end of the program. What was the total number of boys and girls at the beginning of the program?
<pre>
The problem doesn't say that any girls left, so we'll assume that no girls
left, and so there were also g girls at the beginning of the program.

Let x = the number of boys at the beginning of the program.

Then we subtract one-fifth of x from x to get b boys: 

{{{x}}}{{{""-""}}}{{{expr(1/5)x}}}{{{""=""}}}{{{b}}}

Multiply through by 5:

{{{5x-x}}}{{{""=""}}}{{{5b}}}

{{{4x}}}{{{""=""}}}{{{5b}}}

{{{x}}}{{{""=""}}}{{{5b/4}}}

Checking:
There were {{{5b/4}}} boys at the beginning, then {{{expr(1/5)*expr(5b/4)=b/4}}} left,
and so there were {{{5b/4-b/4=4b/4=b}}} boys at the end.

Answer: {{{5b/4}}} boys and g girls at the beginning.

Edwin</pre>