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Finding the Third Proportional to 305,698 and 407,706

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Solution

The third proportional to 305,698 and 407,706 is: 543,752.93

Step by Step Solution

  1. Step 1: Write the proportion equation
    305,698 : 407,706 = 407,706 : x
  2. Step 2: Convert to fraction form
    305,698/407,706 = 407,706/x
  3. Step 3: Cross multiply
    305,698x = 407,706 × 407,706
  4. Step 4: Simplify right side
    305,698x = 166,224,182,436
  5. Step 5: Solve for x
    x = 166,224,182,436/305,698
  6. Step 6: Final answer
    x = 543,752.93

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Why These Related Problems?

These problems maintain the same ratio (1.33) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.