Students at Central School were surveyed regarding lunch choices. Of the students that responded, exactly \(\frac{1}{3}\) wanted more fresh fruits and vegetables. Of those students not wanting more fresh fruits and vegetables, exactly \(\frac{1}{8}\) wanted more seafood. What is the minimum number of students that responded to the survey?
Answer (3)
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. 3 2 ∗ 8 1 = 12 1 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
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.
To find the minimum number of students surveyed, we calculated the fractions of students wanting fruits, vegetables, and seafood. The smallest common multiple that satisfies these fractions is 12. Therefore, the minimum number of students that responded to the survey is 12.
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