Let's break down the problem step by step.

Given information:

• Total students = 100
• Girls = 42, so boys = 100 - 42 = 58
• Girls who cycle = 19
• Boys who walk = 35
• Students who take the bus = 20
  • Girls who take the bus = 9, so boys who take the bus = 20 - 9 = 11

Step 1: Find the number of boys who walk

We are given that 35 boys walk.

Step 2: Find the number of girls who walk

Total students who take the bus = 20, so students who either walk or cycle = 100 - 20 = 80.

• Boys who walk = 35
• Girls who cycle = 19
• Boys who take the bus = 11
• Girls who take the bus = 9

Total girls = 42, and we know that: $\text{Girls who walk} = \text{Total girls} - (\text{Girls who cycle} + \text{Girls who take the bus})$ $= 42 - (19 + 9) = 42 - 28 = 14$ So, 14 girls walk.

Step 3: Find the total number of students who cycle

Total students who walk: $\text{Girls who walk} + \text{Boys who walk} = 14 + 35 = 49$ Since the total number of students is 100, the remaining students must be those who cycle: $\text{Students who cycle} = 100 - (\text{Students who walk} + \text{Students who take the bus})$ $= 100 - (49 + 20) = 100 - 69 = 31$

Final Answer:

The total number of students who cycle to school is 31.

Would you like a detailed breakdown or further clarification?

Here are five related questions to deepen understanding:

1. How many boys cycle to school?
2. What is the percentage of students who cycle?
3. How many more boys than girls walk to school?
4. If 5 more students started taking the bus, how would that affect the number of students cycling?
5. What is the ratio of students who cycle to those who take the bus?

Tip: Always verify your final answer by checking if all given numbers add up to the total!