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Finding the Third Proportional to 180,398 and 256,419

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Solution

The third proportional to 180,398 and 256,419 is: 364,475.79

Step by Step Solution

  1. Step 1: Write the proportion equation
    180,398 : 256,419 = 256,419 : x
  2. Step 2: Convert to fraction form
    180,398/256,419 = 256,419/x
  3. Step 3: Cross multiply
    180,398x = 256,419 × 256,419
  4. Step 4: Simplify right side
    180,398x = 65,750,703,561
  5. Step 5: Solve for x
    x = 65,750,703,561/180,398
  6. Step 6: Final answer
    x = 364,475.79

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Why These Related Problems?

These problems maintain the same ratio (1.42) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.