We are given that the ratio of boys to girls in a school is 3:4, and the total number of children is 161. Let's determine how many boys and girls there are.

Step 1: Define Variables

Let:

• $x$ be the common ratio factor.
• The number of boys = $3x$.
• The number of girls = $4x$.

Step 2: Set Up the Equation

The total number of children is given as 161:
$3x + 4x = 161$ $7x = 161$

Step 3: Solve for $x$

$x = \frac{161}{7} = 23$

Step 4: Find the Number of Boys and Girls

• Boys = $3x = 3(23) = 69$
• Girls = $4x = 4(23) = 92$

Final Answer:

There are 69 boys and 92 girls in the school.

Would you like a verification step or a different explanation?

Here are 5 related problems for practice:

1. If a class has a boy-to-girl ratio of 5:6 and there are 198 students, how many are boys?
2. A group has a ratio of men to women of 2:3. If there are 80 people, how many are women?
3. The ratio of teachers to students in a school is 1:12. If there are 2600 people in total, how many are students?
4. A bag contains red and blue balls in a 3:5 ratio. If there are 64 balls, how many are red?
5. A farm has cows and sheep in a 7:9 ratio. If there are 128 animals, how many are cows?

Tip:

When solving ratio problems, always express the total in terms of the ratio variable before setting up an equation.