Let's break down the problem step by step from the image provided:

Problem summary:

• Three-fifths of the students are girls.
• Half of the boys take the bus to school.
• One-seventh of the girls take the bus to school.
• A total of 147 students do not take the bus to school.

We need to find the total number of students in the class.

Let:

• $x$ be the total number of students in the class.
• $\frac{3}{5}x$ be the number of girls in the class.
• $\frac{2}{5}x$ be the number of boys in the class.

Step 1: Calculate how many boys and girls take the bus.

• Half of the boys take the bus, so $\frac{1}{2} \times \frac{2}{5}x = \frac{1}{5}x$ boys take the bus.
• One-seventh of the girls take the bus, so $\frac{1}{7} \times \frac{3}{5}x = \frac{3}{35}x$ girls take the bus.

Step 2: Calculate how many students do not take the bus.

• The boys who do not take the bus are $\frac{2}{5}x - \frac{1}{5}x = \frac{1}{5}x$.
• The girls who do not take the bus are $\frac{3}{5}x - \frac{3}{35}x = \frac{18}{35}x$.

Step 3: Set up the equation for the students who do not take the bus.

We know 147 students do not take the bus, so: $\frac{1}{5}x + \frac{18}{35}x = 147$

Step 4: Solve for $x$.

To solve this equation, let's find a common denominator: $\frac{1}{5}x = \frac{7}{35}x$ So the equation becomes: $\frac{7}{35}x + \frac{18}{35}x = 147$ $\frac{25}{35}x = 147$ $\frac{5}{7}x = 147$ Multiply both sides by $7$ to get rid of the denominator: $5x = 147 \times 7$ $5x = 1029$ Now, divide both sides by 5: $x = \frac{1029}{5}$ $x = 205.8$

Since the total number of students must be a whole number, we should round it to the closest option from the multiple-choice answers. The closest is 210 students.

Thus, the correct answer is b. 210 students.

Would you like more details on the steps or help with a different problem?

Related questions:

1. What would the equation look like if 4/5 of the students were girls instead of 3/5?
2. How would the answer change if all the boys took the bus to school?
3. What if the number of students not taking the bus was 160 instead of 147?
4. How would the problem change if one-fourth of the girls took the bus instead of one-seventh?
5. Can we calculate the number of students taking the bus if the total number is already known?

Tip:

Always cross-check the total with the conditions in the problem to avoid rounding errors when the final answer must be an integer.