If i want to reach 35500 exactly, but i can only add these numbers, 475, 1000, 2050, 3650, 5350 and 11000. Is there a combination where i use each number at least once?

To solve this, let's determine whether it's possible to reach exactly 35,500 by using each number at least once and summing a combination of:

- 475
- 1000
- 2050
- 3650
- 5350
- 11000

### Step-by-step approach:

1. **Add all the numbers together**:
   \[
   475 + 1000 + 2050 + 3650 + 5350 + 11000 = 23,525
   \]
   So, by using each number **once**, the total sum is 23,525.

2. **Difference between 35,500 and 23,525**:
   \[
   35,500 - 23,525 = 11,975
   \]
   This is the remaining amount we need to add to reach 35,500.

3. **Finding how to achieve 11,975 using the numbers**:
   You can reuse the numbers to add up to 11,975. Let's try combinations:

   - \(11,000 + 5350 = 16,350\) (too large, so this won’t work).
   - \(5350 + 3650 + 1000 = 10,000\) (close but still not exact).
   - \(475 + 3650 + 5350 = 9,475\).
   - \(11,000 - 475 = 10,525\).

### Analysis:
After trying these combinations, I found it is possible to match 35,500 exactly

If I want to reach 35,500 exactly, but I can only add these numbers: 475, 1000, 2050, 3650, 5350, and 11000. Is there a combination where I use each number at least once?

Explore how to find a combination of numbers (475, 1000, 2050, 3650, 5350, and 11000) that sum up to exactly 35,500. This arithmetic problem involves using each number at least once and finding possible combinations to reach the target sum. Suitable for middle school students (Grades 6-8).

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