Question

In a school with only sixth and seventh graders, 2/5 of the 200 students are seventh graders.

A. How many students in the school are seventh graders?
B. Describe two different ways to determine how many students in the school are sixth graders.
C. Of the seventh graders, 30% are in the band. If the band has the same number of sixth graders as seventh graders, what percentage of the sixth graders are in the band? Explain how you found your answer.

Answer 1

To determine the number of seventh graders, multiply the total number of students by the proportion. To determine the number of sixth graders, subtract the number of seventh graders from the total or multiply by the fraction representing the proportion. To find the percentage of sixth graders in the band, divide the number of sixth graders in the band by the total number of sixth graders and multiply by 100%.

Step-by-step explanation:

To determine the number of seventh graders in the school, we can multiply the total number of students (200) by the fraction that represents the proportion of seventh graders (2/5):

Number of seventh graders = 200 x 2/5 = 80

One way to determine the number of sixth graders is to subtract the number of seventh graders from the total number of students:

Number of sixth graders = 200 - 80 = 120

Another way to determine the number of sixth graders is to find the fraction of sixth graders (3/5) and multiply it by the total number of students:

Number of sixth graders = 200 x 3/5 = 120

To calculate the percentage of sixth graders in the band, we need to find the number of sixth graders in the band and divide it by the total number of sixth graders:

Number of sixth graders in the band = Number of seventh graders in the band = 80 x 30/100 = 24

Percentage of sixth graders in the band = Number of sixth graders in the band / Number of sixth graders x 100% = 24 / 120 x 100 = 20%