At Park Junior High, 10%, or 160, of the students, play a musical instrument. How many students attend the school?

Question

A tape diagram. StartFraction part Over whole EndFraction = StartFraction 10 Over 100 EndFraction = StartFraction 160 Over question mark EndFraction

Which statements are correct? Check all that apply.
The total number of students is < 160.
The total number of students is > 160.
The percent as a part-to-whole ratio is StartFraction 10 Over 100 EndFraction.
The percent as a part-to-whole ratio is StartFraction 160 Over 100 EndFraction
There are 1,600 students in the school.
There are 250 students in the school.

Answer 1

To determine how many students attend Park Junior High, we can set up a proportion based on the information given:

Since 10% of the students play a musical instrument, and this 10% is represented by 160 students, we can find the total number of students (the whole) by setting up the equation:

\[ \frac{10}{100} = \frac{160}{x} \]

Where \( x \) is the total number of students. We can cross-multiply to solve for \( x \):

\[ 10x = 160 \times 100 \]

\[ 10x = 16000 \]

\[ x = \frac{16000}{10} = 1600 \]

So the total number of students at Park Junior High is 1,600.

Now evaluating the statements:

1. The total number of students is < 160. - Incorrect
2. The total number of students is > 160. - Correct (because it's 1,600)
3. The percent as a part-to-whole ratio is \( \frac{10}{100} \). - Correct
4. The percent as a part-to-whole ratio is \( \frac{160}{100} \). - Incorrect (the part compares to the total, not 100)
5. There are 1,600 students in the school. - Correct
6. There are 250 students in the school. - Incorrect

Therefore, the correct statements are:

• The total number of students is > 160.
• The percent as a part-to-whole ratio is \( \frac{10}{100} \).
• There are 1,600 students in the school.