Jim and Wanda both have some apples. If Jim gives Wanda an apple, they will both have the same number of apples. However, if Wanda gives Jim an apple, Jim will have twice as many as Wanda. How many apples do Jim and Wanda each have?

Why this works

This riddle is a great example of using algebra to solve a problem involving two people and their apples! Let's break it down: 1. Let’s say Jim has \( J \) apples and Wanda has \( W \) apples. The first condition states that if Jim gives Wanda one apple, they will have the same number of apples. This gives us the equation: \( J - 1 = W + 1 \) or \( J - W = 2 \). 2. The second condition says if Wanda gives Jim an apple, Jim will have twice as many apples as Wanda. This leads to the equation: \( J + 1 = 2(W - 1) \) or rearranged, \( J = 2W - 3 \). Now we have two equations: - \( J - W = 2 \) - \( J = 2W - 3 \) By substituting the first equation into the second, we can solve for \( W \): - From \( J = W + 2 \), substitute into \( J = 2W - 3 \): - \( W + 2 = 2W - 3 \) - Rearranging gives \( W = 5 \). Using \( W = 5 \) in \( J - W = 2 \) gives \( J = 7 \). So, Jim has 7 apples and Wanda has 5 apples. The clever use of equations highlights the logic behind their interactions with the apples!