Let's break down the problem step by step.

Given information:

1. 25% of the balls are green.
2. 45% of the balls are red.
3. The rest (100% - 25% - 45%) = 30% are blue.
4. There are 30 more red balls than blue balls.

We need to find how many green balls are in the box.

Variables:

Let the total number of balls be $x$.

• The number of green balls = $0.25x$.
• The number of red balls = $0.45x$.
• The number of blue balls = $0.30x$.

Step-by-Step Solution:

We know that the number of red balls is 30 more than the number of blue balls, so we can set up the equation:

$0.45x = 0.30x + 30$

Now, let's solve for $x$:

$0.45x - 0.30x = 30$ $0.15x = 30$ $x = \frac{30}{0.15} = 200$

So, the total number of balls $x$ is 200.

Finding the number of green balls:

The number of green balls is 25% of the total:

$\text{Green balls} = 0.25 \times 200 = 50$

Thus, there are 50 green balls in the box.

Would you like more details or have any questions?

Here are 5 related questions to consider:

1. How many red balls are there in the box?
2. How many blue balls are there in the box?
3. What percentage of the balls are either red or green?
4. If the number of blue balls doubled, how many blue balls would there be?
5. What would the new total number of balls be if 10 more green balls were added?

Tip:

When working with percentages, converting them to decimals helps simplify the equation and makes it easier to solve problems involving ratios and proportions.