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Finding the Third Proportional to 97,409 and 209,385

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Solution

The third proportional to 97,409 and 209,385 is: 450,082.42

Step by Step Solution

  1. Step 1: Write the proportion equation
    97,409 : 209,385 = 209,385 : x
  2. Step 2: Convert to fraction form
    97,409/209,385 = 209,385/x
  3. Step 3: Cross multiply
    97,409x = 209,385 × 209,385
  4. Step 4: Simplify right side
    97,409x = 43,842,078,225
  5. Step 5: Solve for x
    x = 43,842,078,225/97,409
  6. Step 6: Final answer
    x = 450,082.42

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Why These Related Problems?

These problems maintain the same ratio (2.15) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.