Answer: Ravi lost \( \frac{1}{3} \) of his marbles and gave Joe \( \frac{1}{4} \) of the remainder. He remained with 48 marbles. How many did he have at first?

Let \( x \) be the total number of marbles Ravi had at first. After losing \( \frac{1}{3} \) of his marbles, he had \( \frac{2}{3}x \) left. He then gave Joe \( \frac{1}{4} \) of the remaining marbles, which is \( \frac{1}{4} \times \frac{2}{3}x = \frac{1}{6}x \). The number of marbles he was left with is: \[ \frac{2}{3}x - \frac{1}{6}x \] To combine these fractions, we find a common denominator of 6: \[ \frac{4}{6}x - \frac{1}{6}x = \frac{3}{6}x = \frac{1}{2}x \] According to the problem, this remaining amount equals 48 marbles: \[ \frac{1}{2}x = 48 \] Multiplying both sides by 2, we find: \[ x = 96 \] So, Ravi initially had 96 marbles. Now, let's dive into some additional fun facts to enrich your learning experience! Ravi's marbles journey connects beautifully with the concept of fractions and rationing, commonly observed in ancient trade practices where items were divided into parts to ensure fair exchange among traders, much like how Ravi distributed his marbles! If you ever find yourself dividing quantities, remember to keep track of your fractions carefully! A common mistake is to forget about the initial totals before division. For instance, always double-check the amount you're starting with after taking away a portion, as it can lead to miscalculating what's left, just like how Ravi almost lost track of his marbles!