Question

Mr. Gumdrop is determining how many of his 8th and 9th students prefer candy, chips, or fruit.

He sent Isabella to survey students and create a frequency table. However, she did not show her work when she calculated the relative frequencies and is missing all of the counts. She only has the count for 8th graders who like chips. How many students did she survey total, rounded to the nearest whole number?

Candy

Chips

Fruit

Grade 8

LaTeX: 27\%

LaTeX: 5=16\%

LaTeX: 10\%

Grade 9

LaTeX: 20\%

LaTeX: 10\%

LaTeX: 17\%

Answer 1

Let's let \( N \) represent the total number of students Mr. Gumdrop surveyed. To find \( N \), we will set up equations based on the percentages provided for the different preferences.

### 8th Grade
For the 8th grade:
- **Candy:** 27% of \( N \)
- **Chips:** 16% of \( N \) (We know that there are 5 students who like chips)
- **Fruit:** 10% of \( N \)

From the chips preference, we note that:
\[
0.16N = 5.
\]
Now we will solve for \( N \):
\[
N = \frac{5}{0.16} = 31.25.
\]

### 9th Grade
For the 9th grade:
- **Candy:** 20% of \( N \)
- **Chips:** 10% of \( N \)
- **Fruit:** 17% of \( N \)

These percentages do not influence the total \( N \) calculation based on our earlier findings for the 8th grade, but we can check if rounding \( N \) to the nearest whole number adds up correctly to the preferences.

### Final Calculation
Rounding \( N \) to the nearest whole number gives:
\[
N \approx 31.
\]

Thus, the total number of students Isabella surveyed is approximately:

\[
\boxed{31}.
\]