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Finding the Third Proportional to 580.78 and 819.42

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Solution

The third proportional to 580.78 and 819.42 is: 1,156.12

Step by Step Solution

  1. Step 1: Write the proportion equation
    580.78 : 819.42 = 819.42 : x
  2. Step 2: Convert to fraction form
    580.78/819.42 = 819.42/x
  3. Step 3: Cross multiply
    580.78x = 819.42 × 819.42
  4. Step 4: Simplify right side
    580.78x = 671,452.21
  5. Step 5: Solve for x
    x = 671,452.21/580.78
  6. Step 6: Final answer
    x = 1,156.12

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Why These Related Problems?

These problems maintain the same ratio (1.41) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.