Question

In a class there were more than 10 boys than a certain number of girls. After 40% of the girls and 60% of the boys left, the remaining number of girls were 8 more than the remaining boys. Find the possible number of students initially in the class.

Hint:

For problems involving inequalities and integer solutions, solve for one variable first. Then, use the integer constraint to find the smallest possible valid value or a range of values.

Answer 1

Correct Answer: 135

Step 1: Let girls \(=g\), boys \(=g+10\) (boys exceed girls by \(10\)).
Step 2: After the departures, girls remaining \(=0.6g\), boys remaining \(=0.4(g+10)\), and girls remaining is \(8\) more than boys remaining: \[ 0.6g-0.4(g+10)=8. \]
Step 3: Simplify: \(0.6g-0.4g-4=8 \implies 0.2g=12 \implies g=60\), so boys \(=70\).
Step 4: Total initial students: \[ \boxed{60+70=130} \]