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Finding the Third Proportional to 210,414 and 289,269

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Solution

The third proportional to 210,414 and 289,269 is: 397,675.79

Step by Step Solution

  1. Step 1: Write the proportion equation
    210,414 : 289,269 = 289,269 : x
  2. Step 2: Convert to fraction form
    210,414/289,269 = 289,269/x
  3. Step 3: Cross multiply
    210,414x = 289,269 × 289,269
  4. Step 4: Simplify right side
    210,414x = 83,676,554,361
  5. Step 5: Solve for x
    x = 83,676,554,361/210,414
  6. Step 6: Final answer
    x = 397,675.79

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Why These Related Problems?

These problems maintain the same ratio (1.37) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.