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Finding the Third Proportional to 4,114 and 9,685

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Solution

The third proportional to 4,114 and 9,685 is: 22,800.01

Step by Step Solution

  1. Step 1: Write the proportion equation
    4,114 : 9,685 = 9,685 : x
  2. Step 2: Convert to fraction form
    4,114/9,685 = 9,685/x
  3. Step 3: Cross multiply
    4,114x = 9,685 × 9,685
  4. Step 4: Simplify right side
    4,114x = 93,799,225
  5. Step 5: Solve for x
    x = 93,799,225/4,114
  6. Step 6: Final answer
    x = 22,800.01

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Why These Related Problems?

These problems maintain the same ratio (2.35) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.