To solve the problem, we can break it down into steps:

Step 1: Analyze the Initial Situation

• The initial number of blue balls = 18.
• After adding 32 blue balls, the total number of blue balls in the box = $18 + 32 = 50$.

Step 2: Set Up the Ratio for the Pink Balls

Let the initial number of pink balls be $p$.

• After adding 48 pink balls, the total number of pink balls in the box = $p + 48$.

According to the problem, the ratio of pink balls to blue balls becomes 3:2 after adding these balls. Therefore, we have:

$\frac{p + 48}{50} = \frac{3}{2}$

Step 3: Solve for $p$

To find $p$, cross-multiply and solve the equation:

$2(p + 48) = 3 \times 50$

$2p + 96 = 150$

$2p = 150 - 96 = 54$

$p = \frac{54}{2} = 27$

So, the initial number of pink balls was $27$.

Step 4: Find the Number of Pink Balls to Add for the 2:1 Ratio

Now, we need to find how many additional pink balls $x$ are needed to make the ratio 2:1.

The total number of blue balls is $50$, and the total number of pink balls will be $27 + 48 + x$. We want:

$\frac{27 + 48 + x}{50} = \frac{2}{1}$

$27 + 48 + x = 100$

$75 + x = 100$

$x = 100 - 75 = 25$

Final Answer

You would need to add 25 more pink balls to make the ratio of pink balls to blue balls 2:1.

Would you like more details or have any questions about the solution?

Here are some related questions:

1. What if the initial number of blue balls were different, how would that affect the ratio?
2. How would the problem change if the ratio after adding the balls was 4:3 instead of 3:2?
3. What is the total number of balls in the box after the first set of additions?
4. Can you generalize the formula to find how many balls need to be added to achieve any desired ratio?
5. How would the problem be solved if some balls were removed instead of added?

Tip: When dealing with ratios, remember that cross-multiplication is a powerful tool to simplify and solve equations quickly.