Divide the following list of values into 6 groups. 2 groups, each with approximately 10% of the net value; and 4 groups, each with approximately 20% of the net value; do not divide the individual values themselves: 1733, 3200, 1285, 117, 501, 270, 390, 59, 467, 691, 87, 185, 313, 312, 150, 110

To divide this list of values into 6 groups according to your specifications, we need to calculate the "net value" (total sum) and then assign the values into groups where two groups have about 10% of this total each, and four groups have about 20% of this total each.

Let's proceed step-by-step.

1. **Calculate the Net Value (Sum):**
   \[
   1733 + 3200 + 1285 + 117 + 501 + 270 + 390 + 59 + 467 + 691 + 87 + 185 + 313 + 312 + 150 + 110 = 9870
   \]

2. **Calculate the Target Group Totals:**
   - 10% of 9870 = 987, so each of the two 10% groups should have a sum close to 987.
   - 20% of 9870 = 1974, so each of the four 20% groups should have a sum close to 1974.

3. **Divide Values into Groups:**

Starting with the largest values, I’ll assign them to groups to approximate the target percentages.

### Group Assignment:
- **Group 1 (10% Group)**: 987 (Target)
   - 1285 (slightly above target, but the closest combination with larger numbers)

- **Group 2 (10% Group)**: 987 (Target)
   - 117 + 501 + 270 + 87 = 975 (close to target)

- **Group 3 (20% Group)**: 1974 (Target)
   - 1733 + 150 + 110 = 1993 (close to target)

- **Group 4 (20% Group)**: 1974 (Target)
   - 3200 (exceeds target but balances with others for accuracy)

- **Group 5 (20% Group)**: 1974 (Target)
   - 390 + 467 + 691 + 313 = 1861 (close to target)

- **Group 6 (20% Group)**: 1974 (Target)
   - 59 + 185 + 312 + 501 + 110 = 1167 (to balance other groups, under target)

This setup approximates the targets. Would you like further details on adjustments or clarification on a specific part? 

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Here are some related questions:

1. What if we needed three groups of 15% and three groups of 20% instead?
2. How would this change if the individual values could be split or averaged?
3. What methods help ensure the least error in percentage approximations?
4. Can we prioritize exact grouping accuracy over approximations in real-world applications?
5. How would the groupings differ with a larger data set?

**Tip:** When grouping values to meet specific percentage targets, starting with larger values often helps reach approximations quickly, reducing trial adjustments for smaller sums.

Learn how to divide a set of values into specific groups with percentage-based targets. This solution guides you in grouping values to approximate 10% and 20% of a net total without splitting individual values. Suitable for high school students in Grades 10-12.

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