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Finding the Third Proportional to 99,749 and 213,509

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Solution

The third proportional to 99,749 and 213,509 is: 457,008.02

Step by Step Solution

  1. Step 1: Write the proportion equation
    99,749 : 213,509 = 213,509 : x
  2. Step 2: Convert to fraction form
    99,749/213,509 = 213,509/x
  3. Step 3: Cross multiply
    99,749x = 213,509 × 213,509
  4. Step 4: Simplify right side
    99,749x = 45,586,093,081
  5. Step 5: Solve for x
    x = 45,586,093,081/99,749
  6. Step 6: Final answer
    x = 457,008.02

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Why These Related Problems?

These problems maintain the same ratio (2.14) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.