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Finding the Third Proportional to 212,099 and 457,407

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Solution

The third proportional to 212,099 and 457,407 is: 986,431.64

Step by Step Solution

  1. Step 1: Write the proportion equation
    212,099 : 457,407 = 457,407 : x
  2. Step 2: Convert to fraction form
    212,099/457,407 = 457,407/x
  3. Step 3: Cross multiply
    212,099x = 457,407 × 457,407
  4. Step 4: Simplify right side
    212,099x = 209,221,163,649
  5. Step 5: Solve for x
    x = 209,221,163,649/212,099
  6. Step 6: Final answer
    x = 986,431.64

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Why These Related Problems?

These problems maintain the same ratio (2.16) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.