Let's break this problem into manageable parts to calculate the number of students who cycle to school.

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Step-by-step solution:

1. Total Students:

   • There are 100 students in total.

2. Number of Girls and Boys:

   • 42 are girls, so the remaining $100 - 42 = 58$ are boys.

3. Students Taking the Bus:

   • There are 20 students who take the bus.
   • Among these, 9 are girls, so the remaining $20 - 9 = 11$ are boys.

4. Students Walking:

   • 35 boys walk to school.
   • Since 35 boys walk, the total number of boys cycling or taking the bus is $58 - 35 = 23$.

5. Students Cycling:

   • 19 girls cycle to school.
   • To find the total number of students cycling to school:
     • Total students cycling = Total students - (Students walking + Students taking the bus)
     • $100 - (35 + 20) = 45.$
   • Since we know 19 girls cycle to school, the number of boys cycling is:
     • $45 - 19 = 26.$

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Final Answer:

The number of students who cycle to school is 45.

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Would you like me to clarify any part of this solution or explore related scenarios?

Related Questions:

1. How many students walk to school?
2. What percentage of the students cycle to school?
3. How many boys take the bus or cycle?
4. What fraction of girls cycle to school?
5. How can this problem be represented with a Venn diagram?

Tip:

Always verify by ensuring the sum of all categories equals the total number of students in the problem.