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Finding the Third Proportional to 257,934 and 398,409

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Solution

The third proportional to 257,934 and 398,409 is: 615,388.94

Step by Step Solution

  1. Step 1: Write the proportion equation
    257,934 : 398,409 = 398,409 : x
  2. Step 2: Convert to fraction form
    257,934/398,409 = 398,409/x
  3. Step 3: Cross multiply
    257,934x = 398,409 × 398,409
  4. Step 4: Simplify right side
    257,934x = 158,729,731,281
  5. Step 5: Solve for x
    x = 158,729,731,281/257,934
  6. Step 6: Final answer
    x = 615,388.94

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Why These Related Problems?

These problems maintain the same ratio (1.54) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.