Question

There are 70 students in the school band. 40% of them are sixth graders, 20% are seventh graders, and the rest are eighth graders. How many band members are sixth graders? How many band members are seventh graders? What percentage of the band members are eighth graders?

Answer 1

Answer:

The band members of sixth graders are 28.

The band members of seventh graders are 14.

The percentage of the  band members eighth graders are 40% .

Step-by-step explanation

Formula

$Percentage = \frac{Part\ value\times 100}{Total\ value}$

As given

There are 70 students in the school band.

40% of them are sixth graders, 20% are seventh graders, and the rest are eighth graders.

Now first find out the  band members are sixth graders .

Percentage = 40%

Total value = 70

Put in the formula

$40 = \frac{Number\ of\ band\ members\ are\ sixth\ graders\times 100}{70}$

$Number\ of\ band\ members\ are\ sixth\ graders = \frac{40\times 70}{100}$

$Number\ of\ band\ members\ are\ sixth\ graders = \frac{2800}{100}$

$Number\ of\ band\ members\ are\ sixth\ graders = 28$

Therefore the number of band members are from sixth graders are 28 .

Now first find out the  band members are seventh graders .

Percentage = 20%

Total value = 70

$20 = \frac{Number\ of\ band\ members\ are\ seventh\ graders\times 100}{70}$

$Number\ of\ band\ members\ are\ seventh\ graders = \frac{20\times 70}{100}$

$Number\ of\ band\ members\ are\ seventh\ graders = \frac{1400}{100}$

$Number\ of\ band\ members\ are\ seventh\ graders = 14$

Therefore the number of band members are from seventh graders are 14.

Now find out the percentage of the eighth graders of the band members.

Total number of band members = sixth graders members + seventh grade members + eighth graders members

As  sixth graders members =  28

seventh grade members = 14

Total number of band members = 70

Put in the above

70 = 28 + 14  + eighth graders members

70 - 42 = eighth graders members

28 = eighth graders members

Put in the percentage formula

$Percentage = \frac{28\times 100}{70}$

$Percentage = \frac{2800}{70}$

Percentage = 40%

Therefore the percentage of the band members are eighth graders is 40 %.