Question

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 1

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.

Answer 2

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.
`(2)/(3) * (1)/(8) = (1)/(12)` 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