You need to find a way to combine the given amounts so that the total equals 50,105.10 and 4,495.02, with each amount being used only once.

Here are the amounts provided:

35,125.58
228.24
310.54
1,177.02
598.97
1,039.35
10,669.44
2,848.14
484.11
1,010.63
1,108.10

To solve this, I need to find combinations of the given amounts that sum up to either **50,105.10** or **4,495.02**. The goal is to use each amount exactly once. I'll break it down systematically by testing possible combinations.

### Provided Amounts:
- 35,125.58
- 228.24
- 310.54
- 1,177.02
- 598.97
- 1,039.35
- 10,669.44
- 2,848.14
- 484.11
- 1,010.63
- 1,108.10

### Approach:
1. Start with the largest amounts to try and sum up to 50,105.10.
2. Whatever is left over should hopefully sum to 4,495.02.
3. Verify if each amount is used exactly once.

Let's try this by checking combinations.

I'll calculate the sums now.Here are the combinations that sum to the given totals:

1. **For 50,105.10**, the combination is:
   - 35,125.58
   - 1,177.02
   - 598.97
   - 1,039.35
   - 10,669.44
   - 484.11
   - 1,010.63

2. **For 4,495.02**, the combination is:
   - 228.24
   - 310.54
   - 2,848.14
   - 1,108.10

Each amount is used exactly once, and the totals are correct.

Would you like further details or have any questions?

### Related Questions:
1. How can I verify the sum of combinations mathematically?
2. What if there are more than two target totals to reach?
3. How can I approach such problems with a larger set of amounts?
4. Are there alternative methods to solve this using fewer steps?
5. What happens if no exact combinations exist?

**Tip:** When dealing with multiple sums, starting with the largest numbers can help reduce the number of combinations to test.

You need to find a way to combine the given amounts so that the total equals 50,105.10 and 4,495.02, with each amount being used only once. Here are the amounts provided: 35,125.58, 228.24, 310.54, 1,177.02, 598.97, 1,039.35, 10,669.44, 2,848.14, 484.11, 1,010.63, 1,108.10.

Learn how to combine given amounts so that they sum up to exactly 50,105.10 and 4,495.02. The solution involves combinatorics, summation of elements from a set, and combinatorial optimization. Ideal for high school students and math enthusiasts.

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