Question

Franklin Middle School's spring concert is next week. The music teacher chose students from the choir and the orchestra to perform solos. There are 25 choir students, and 5 of them have a solo. There are 20 orchestra students, and 4 of them have a solo. Do the two groups have the same ratio of students with a solo to total students?

Answer 1

To determine if the two groups have the same ratio of students with a solo to total students, we will calculate the ratio for each group.

For the choir:

• Total choir students = 25
• Students with a solo = 5

The ratio of choir students with a solo to total choir students is: \[ \text{Ratio for choir} = \frac{\text{Students with a solo}}{\text{Total choir students}} = \frac{5}{25} = \frac{1}{5} \]

For the orchestra:

• Total orchestra students = 20
• Students with a solo = 4

The ratio of orchestra students with a solo to total orchestra students is: \[ \text{Ratio for orchestra} = \frac{\text{Students with a solo}}{\text{Total orchestra students}} = \frac{4}{20} = \frac{1}{5} \]

Now, we can compare the two ratios:

• Ratio for choir = \(\frac{1}{5}\)
• Ratio for orchestra = \(\frac{1}{5}\)

Since both ratios are equal, we conclude that the two groups do have the same ratio of students with a solo to total students.