When one-fifth of the boys left, there were still b boys and g girls who stayed to see a program. What was the total number of boys and girls at the beginning of the program?

The number of boys at the beginning is equal to the number of boys currently present (b) plus 1/5 of the boys that were present in the beginning. That is, (b + 1/5b) is the number of boys that were present in the beginning of the program. The number of girls present now is the same as the number of girls present at the beginning of the program. Therefore (b + 1/5b) + g = the number of boys and girls present at the beginning of the program.