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Finding the Third Proportional to 102,454 and 209,965

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Solution

The third proportional to 102,454 and 209,965 is: 430,293.61

Step by Step Solution

  1. Step 1: Write the proportion equation
    102,454 : 209,965 = 209,965 : x
  2. Step 2: Convert to fraction form
    102,454/209,965 = 209,965/x
  3. Step 3: Cross multiply
    102,454x = 209,965 × 209,965
  4. Step 4: Simplify right side
    102,454x = 44,085,301,225
  5. Step 5: Solve for x
    x = 44,085,301,225/102,454
  6. Step 6: Final answer
    x = 430,293.61

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Why These Related Problems?

These problems maintain the same ratio (2.05) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.