Let the total number of balls in the box be denoted by $N$. We are given the following information:

• 25% of the balls are green, so the number of green balls is $0.25N$.
• 45% of the balls are red, so the number of red balls is $0.45N$.
• The rest are blue, so $1 - 0.25 - 0.45 = 0.30$, meaning 30% of the balls are blue, so the number of blue balls is $0.30N$.
• There are 30 more red balls than blue balls, so: $0.45N = 0.30N + 30$

Step 1: Solve for $N$

Subtract $0.30N$ from both sides: $0.45N - 0.30N = 30$ $0.15N = 30$ Now, divide by 0.15: $N = \frac{30}{0.15} = 200$

Step 2: Calculate the number of green balls

The number of green balls is 25% of the total number of balls: $0.25N = 0.25 \times 200 = 50$

Final Answer:

There are 50 green balls in the box.

Would you like further details or have any questions?

Here are 5 related questions to expand your understanding:

1. How many red balls are in the box?
2. How many blue balls are in the box?
3. If there were 40 more green balls, how would that affect the total number of balls?
4. What is the ratio of red to blue balls?
5. What percentage of the balls are not red?

Tip: Always check if the total percentage adds up to 100% to ensure your problem setup is correct!