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Finding the Third Proportional to 214,416 and 409,392

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Solution

The third proportional to 214,416 and 409,392 is: 781,666.53

Step by Step Solution

  1. Step 1: Write the proportion equation
    214,416 : 409,392 = 409,392 : x
  2. Step 2: Convert to fraction form
    214,416/409,392 = 409,392/x
  3. Step 3: Cross multiply
    214,416x = 409,392 × 409,392
  4. Step 4: Simplify right side
    214,416x = 167,601,809,664
  5. Step 5: Solve for x
    x = 167,601,809,664/214,416
  6. Step 6: Final answer
    x = 781,666.53

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Why These Related Problems?

These problems maintain the same ratio (1.91) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.