1

Problem

In State X, Mr. Camp’s eighth-grade class, consisting of 26 students, was surveyed, and 34.6 percent of the students reported that they had at least two siblings. The average eighth‑grade class size in the state is 26. If the students in Mr. Camp’s class are representative of students in the state’s eighth-grade classes and there are 1,800 eighth-grade classes in the state, which of the following best estimates the number of eighth‑grade students in the state who have fewer than two siblings?

2

Step

Calculate the total number of eighth-grade students in the state:

→ There are 1,800 eighth-grade classes in the state
→ The average class size is 26 students
\$"Total number of eighth-grade students" = 1,800 \times 26\$ = 46,800

3

Step

Determine the proportion of students who have fewer than two siblings:

→ In Mr. Camp’s class, 34.6% of the students reported having at least two siblings.
→ Therefore, the percentage of students who have fewer than two siblings is: 100% − 34.6% = 65.4% .

4

Step

Calculate the number of students who have fewer than two siblings:

→ The proportion of students with fewer than two siblings is 65.4%. → Apply this proportion to the total number of eighth-grade students:
\$"Number of students with fewer than two siblings" = 65.4% \times 46,800\$
→ Convert the percentage to decimal for the calculation: 65.4% = 0.654

\$"Number of students with fewer than two siblings" = 0.654 \times 46,800\$
Number of students with fewer than two siblings = 30,607.2

5

Solution

We need to choose the closest estimate from the given options, so the best estimate is 30,600.

6

Sumup

Please summarize steps

Choices

7

Choice-A

This number is significantly lower than our calculation of 30,607.2. It represents only about 34.6% of the total students, which would be the percentage of students with at least two siblings, not fewer than two siblings

Wrong 16,200

8

Choice-B

This number is closer to the middle but still considerably lower than our calculated result. It does not align with our calculation based on 65.4% of the total students

Wrong 23,400

9

Choice-C

This is very close to our calculated number of 30,607.2, making it the most accurate and possible estimate

Correct 30,600

10

Choice-D

This option would imply that all students have fewer than two siblings, which contradicts the information that 34.6% have at least two siblings

Wrong 46,800

11

Answer

Option

C

12

Sumup

Please summarize choices