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Finding the Third Proportional to 397 and 506.50

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Solution

The third proportional to 397 and 506.50 is: 646.20

Step by Step Solution

  1. Step 1: Write the proportion equation
    397 : 506.50 = 506.50 : x
  2. Step 2: Convert to fraction form
    397/506.50 = 506.50/x
  3. Step 3: Cross multiply
    397x = 506.50 × 506.50
  4. Step 4: Simplify right side
    397x = 256,542.25
  5. Step 5: Solve for x
    x = 256,542.25/397
  6. Step 6: Final answer
    x = 646.20

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Why These Related Problems?

These problems maintain the same ratio (1.28) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.