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At Park Junior High, 10%, or 160 students, play a musical instrument. Which statements are correct? Select the three that apply.

A. The percent as a part-to-whole ratio is [tex]\frac{10}{100}[/tex].

B. There are 250 students in the school.

C. The percent as a part-to-whole ratio is [tex]\frac{160}{100}[/tex].

D. The total number of students is > 160.

E. There are 1,600 students in the school.

F. The total number of students is < 160.

Answer :

Let's work through the problem step by step:

1. Determine the Total Number of Students:
We know that 10% of the students at Park Junior High play a musical instrument, and this amounts to 160 students. To find the total number of students, we use the formula:

[tex]\[
\text{Total students} = \frac{\text{Number of students playing instruments}}{\text{Percentage as a decimal}}
\][/tex]

In this case, the percentage as a decimal is [tex]\(\frac{10}{100} = 0.1\)[/tex]. Plug the values into the formula:

[tex]\[
\text{Total students} = \frac{160}{0.1} = 1600
\][/tex]

2. Evaluate Each Statement:

- The percent as a part-to-whole ratio is [tex]\(\frac{10}{100}\)[/tex]:
This statement is correct. The percentage 10% is written as the ratio [tex]\(\frac{10}{100}\)[/tex].

- There are 250 students in the school:
This statement is incorrect. As calculated, the total number of students is 1600.

- The percent as a part-to-whole ratio is [tex]\(\frac{160}{100}\)[/tex]:
This statement is incorrect. The ratio [tex]\(\frac{160}{100}\)[/tex] is not correct for the percentage. It should be [tex]\(\frac{10}{100}\)[/tex].

- The total number of students is [tex]\(>160\)[/tex]:
This statement is correct. Since there are 1600 students as calculated, it is indeed greater than 160.

- There are 1,600 students in the school:
This statement is correct. Our calculation showed that there are 1600 students.

- The total number of students is [tex]\(<160\)[/tex]:
This statement is incorrect. We found the total number to be 1600, which is greater than 160.

So, the three correct statements are:
- The percent as a part-to-whole ratio is [tex]\(\frac{10}{100}\)[/tex].
- The total number of students is [tex]\(>160\)[/tex].
- There are 1,600 students in the school.

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