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Please solve the middle question with steps

aditibishnoi

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20 Jun 2017, 13:59

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OptimusPrepJanielle

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aditibishnoi

I would be happy to help. However, it would have been great if could have typed the question.

Total students = Band only + Orchestra only + Both band and orchestra;

Given, Band only + Orchestra only = 80% and Band only = 50%
Hence Orchestra only = 30%.

Hence total students in Band = 100% Orchestra only = 70%
We are told that 70% of Total students = 119

Hence Total students = 170
Orchestra only = 30% of 170 = 51.

Correct Option: B

it is always a best practice to search for a question before posting it again

aditibishnoi

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How do I search for the question?

aditibishnoi

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It is written tht 50% of total is 119. And not 70%.
How did you get tht?

aditibishnoi

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Also I'd like to mention that there are no formulas given for posting through an app.
An image sign is given,hence I took a picture of the question instead of typing it.

OptimusPrepJanielle

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You can search for any question form the search bar by typing in a few words of the question.
Regarding the question, it says that 50% on the students are in Band only.

Hope this helps!

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Hi,
Please see the solution in the image. Let me know if you need further clarification.
Thanks,

Attachments

New Doc 12_1.jpg [ 712 KiB | Viewed 1387 times ]

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Band Not Band Total
Orch a b
Not O c d
Total 119 x

What you have from the question, write down:
c + b = 0.8x (80% of students are only in 1 group)
a + c = 119 (a + c are students in band, not 0)
c = 0.5x (50% of students are band only)
a + b + c = x (all of students are in band, or or both, that means d = 0)

Solve you have: b = 0.8x - 0.5x = 0.3x (1)
a + b + c = x <=> 119 - c + b + c = x <=> b = x - 119 (2)
From (1) and (2) you have b = 51. Answer B

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