Problem
A fruit vendor had a certain number of apples for sale at the beginning of the day. The first customer that day purchased 3 apples plus $\frac{1}{4}$ of the apples that the vendor had for sale. The second customer purchased 1 apple plus $\frac{1}{3}$ of the apples that remained after the first customer's purchase. If 11 apples remained after the second customer's purchase, how many apples did the fruit vendor have for sale at the beginning of the day?
Solution
Step 1 ：Let x be the number of apples at the beginning. After the first customer's purchase, the vendor had \(x - 3 - \frac{1}{4}x\) apples left. After the second customer's purchase, the vendor had 11 apples left. So, we can write the equation: \[11 = \left(x - 3 - \frac{1}{4}x\right) - \left(1 + \frac{1}{3}\left(x - 3 - \frac{1}{4}x\right)\right)\]
Step 2 ：Solve the equation for x: \[x = 28\]
Step 3 ：\boxed{\text{Final Answer: The fruit vendor had 28 apples for sale at the beginning of the day.}}
