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Finding the Third Proportional to 398 and 431

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Solution

The third proportional to 398 and 431 is: 466.74

Step by Step Solution

  1. Step 1: Write the proportion equation
    398 : 431 = 431 : x
  2. Step 2: Convert to fraction form
    398/431 = 431/x
  3. Step 3: Cross multiply
    398x = 431 × 431
  4. Step 4: Simplify right side
    398x = 185,761
  5. Step 5: Solve for x
    x = 185,761/398
  6. Step 6: Final answer
    x = 466.74

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Why These Related Problems?

These problems maintain the same ratio (1.08) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.