How many apples should be REMOVED so that the fraction of apples in the bowl becomes 1/4 of the total number of fruits?

Answer

To solve the problem, we start with the current counts of apples and bananas. Initially, there are 6 apples and 6 bananas, giving a total of 12 fruits. We want the fraction of apples in the bowl to be 1/4 of the total number of fruits. Let’s denote the number of apples to be removed as x. After removing x apples, the number of apples left will be (6 - x). The new total number of fruits will then be (12 - x), since we are only removing apples and not bananas. We set up the equation: \( \frac{6 - x}{12 - x} = \frac{1}{4} \) To eliminate the fraction, we can cross-multiply: \( 4(6 - x) = 1(12 - x) \) Expanding both sides gives: \( 24 - 4x = 12 - x \) Now, let's rearrange the equation to isolate x: \( 24 - 12 = 4x - x \) \( 12 = 3x \) \( x = 4 \) Thus, we need to remove 4 apples. Verification: - After removing 4 apples from the initial 6, we have \( 6 - 4 = 2 \) apples remaining. - The total number of fruits now will be \( 12 - 4 = 8 \). - The fraction of apples is now \( \frac{2}{8} = \frac{1}{4} \), which matches the requirement. Therefore, the answer is 4. So the answer is option C: 4.