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Finding the Third Proportional to 259,742 and 414,947

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Solution

The third proportional to 259,742 and 414,947 is: 662,892.46

Step by Step Solution

  1. Step 1: Write the proportion equation
    259,742 : 414,947 = 414,947 : x
  2. Step 2: Convert to fraction form
    259,742/414,947 = 414,947/x
  3. Step 3: Cross multiply
    259,742x = 414,947 × 414,947
  4. Step 4: Simplify right side
    259,742x = 172,181,012,809
  5. Step 5: Solve for x
    x = 172,181,012,809/259,742
  6. Step 6: Final answer
    x = 662,892.46

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Why These Related Problems?

These problems maintain the same ratio (1.60) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.