Students at Central School were surveyed regarding lunch choices. Of the students that responded, exactly 1/3 wanted more fresh fruits and vegetables as
choices. Of those students not wanting more fresh fruits and vegetables, exactly 1/8 wanted more seafood. What is the minimum number of students that responded to the survey?

Question

23-11-2014
Mathematics

Answered

Students at Central School were surveyed regarding lunch choices. Of the students that responded, exactly 1/3 wanted more fresh fruits and vegetables as
choices. Of those students not wanting more fresh fruits and vegetables, exactly 1/8 wanted more seafood. What is the minimum number of students that responded to the survey?

Answer :

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MichaelLiu MichaelLiu · Answer 1 · 2014-11-23T22:40:40-05:00

If 1/3 of the students wanted more fruits and veggies, then that means that 2/3 did not. And of that 2/3, 1/8 of them wanted more seafood. [tex] \frac{2}{3} * \frac{1}{8} = \frac{1}{12} [/tex] This means that 1/12 of all the students surveyed wanted more seafood and 1/3 wanted more fruits and veggies. The least common multiple of 3 and 12 (or the LCD of the two fractions) would be 12.
Multiplying by 12, we figure out that 4 of them would have wanted more fruits and veggies and only 1 lonely kid wanted more seafood.
Final answer : 12

MicahSE MicahSE · Answer 2 · 2014-11-23T22:41:25-05:00

MicahSE MicahSE

23-11-2014

1/3 wanted more fresh fruits, which means the 2/3 did not. Of these 2/3s, 1/8 wanted seafood. 1/8 of 2/3 is 2/24, which is 1/12, meaning the minimum number of people that could have responded is 12.

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