<think>Okay, so Mark has a garden with flowers in three colors: yellow, purple, and green. The problem states there are 10 yellow flowers. Then, there are 80% more purple ones than yellow. Finally, the green flowers are only 25% as many as the combined total of yellow and purple. The question is asking for the total number of flowers in the garden.

Alright, let's start by noting down the given values first. Yellow flowers are 10. That part is straightforward. Now, for the purple flowers, there's an 80% increase over the yellow ones. Hmm, percentage increases sometimes trip people up. So, if I have 10 yellow flowers and there are 80% more purple ones, that means the number of purple flowers is the original amount (yellow) plus 80% of that amount.

Calculating 80% of 10: 0.8 * 10 = 8. So, adding that to the original 10 gives 10 + 8 = 18 purple flowers. Let me check if that's correct. Alternatively, another way to compute a percentage increase is to multiply the original amount by (1 + the percentage as a decimal). So here, 10 * (1 + 0.8) = 10 * 1.8 = 18. Yeah, same result. So that's consistent. So 18 purple flowers.

Next, green flowers are 25% as many as yellow and purple combined. So first, we need the total number of yellow and purple flowers. Yellow is 10, purple is 18, so combined that's 10 + 18 = 28. Then 25% of that is the number of green flowers. Calculating 25% of 28: 0.25 * 28. Let me do this step by step. 28 divided by 4 is 7, since 25% is a quarter. So yes, 0.25 * 28 = 7 green flowers.

Therefore, adding all three colors together: 10 yellow + 18 purple + 7 green. Let me compute that. 10 + 18 is 28, then 28 + 7 is 35. So, total flowers are 35. 

Wait a second, let's verify all steps again to be sure there are no mistakes. First, 10 yellow flowers. Purple are 80% more than yellow. 80% of 10 is 8, so 10 + 8 = 18. Then, green is 25% of (10 +18). 25% of 28 is indeed 7. Then total is 10 + 18 +7 = 35. 

Hmm, seems straightforward, but let me try another way. Maybe converting percentage into fractions? Let's see. 80% is equivalent to 4/5. So 80% of 10 is 4/5*10 = 8. So purple is 10 + 8 =18. Then, green is 25% (which is 1/4) of (10+18)=28. So 28*1/4 =7. Then total is 10+18+7=35. Still the same answer. So, that seems correct. 

Alternatively, maybe there's a different interpretation. But looking at the wording: "80% more of those in purple." That should mean purple is 80% more than yellow. Similarly, green is 25% as many as yellow and purple combined. 

Alternatively, someone might misinterpret "80% more of those in purple" as purple being 80% of yellow, but that would be 0.8*10=8, but that's not 80% more—it's 80% of. So, the key difference here is "more than" versus "of". As written, since it's "80% more of those in purple," I think it's 80% more than the yellow. So, as the standard percentage increase. So that would lead to 18 purple.

Similarly, "25% as many green flowers as there are yellow and purple flowers"—again, 25% of the total of yellow and purple. So that's a straight percentage of the combined number.

Therefore, each step checks out correctly.

So, step by step:

1. Yellow flowers: 10

2. Purple flowers: 10 + (80% of 10) = 10 +8=18

3. Green flowers:25% of (10 +18)=25% of 28=7

Total flowers: 10+18+7=35

Thus, the answer should be 35.
</think>

1. **Yellow Flowers**: Given as 10.
2. **Purple Flowers**: 80% more than yellow. Calculating 80% of 10:  
   \(10 \times 0.8 = 8\).  
   Purple flowers = \(10 + 8 = 18\).
3. **Green Flowers**: 25% of the total yellow and purple.  
   Combined yellow and purple: \(10 + 18 = 28\).  
   25% of 28: \(28 \times 0.25 = 7\).
4. **Total Flowers**:  
   \(10 \, (\text{yellow}) + 18 \, (\text{purple}) + 7 \, (\text{green}) = 35\).

**Verification**:  
Re-checking percentages confirms correctness:  
- 80% increase on 10→18 ✔️  
- 25% of 28→7 ✔️  
Summing to 35 is consistent.

**Final Answer**: \boxed{35}