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Finding the Third Proportional to 308,823 and 461,416

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Solution

The third proportional to 308,823 and 461,416 is: 689,406.96

Step by Step Solution

  1. Step 1: Write the proportion equation
    308,823 : 461,416 = 461,416 : x
  2. Step 2: Convert to fraction form
    308,823/461,416 = 461,416/x
  3. Step 3: Cross multiply
    308,823x = 461,416 × 461,416
  4. Step 4: Simplify right side
    308,823x = 212,904,725,056
  5. Step 5: Solve for x
    x = 212,904,725,056/308,823
  6. Step 6: Final answer
    x = 689,406.96

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Why These Related Problems?

These problems maintain the same ratio (1.49) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.