In a working group of a class project, the number of boys is 3 fewer than twice the number of girls. If one boy were replaced by a girl, there would be an equal number of boys and girls in the group. How many students are in the class?
Explanation: Let the number of girls be \(x\). Number of boys is \(2x-3\). If one boy is replaced by a girl, new number of boys is \(2x-3-1 = 2x-4\) and new number of girls is \(x+1\). Since the numbers are equal: \(2x-4 = x+1 \Rightarrow x = 5\). Number of girls is 5, number of boys is \(2(5)-3=7\). Total students \(5+7=12\).
