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Finding the Third Proportional to 686.05 and 822.74

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Solution

The third proportional to 686.05 and 822.74 is: 986.66

Step by Step Solution

  1. Step 1: Write the proportion equation
    686.05 : 822.74 = 822.74 : x
  2. Step 2: Convert to fraction form
    686.05/822.74 = 822.74/x
  3. Step 3: Cross multiply
    686.05x = 822.74 × 822.74
  4. Step 4: Simplify right side
    686.05x = 676,893.46
  5. Step 5: Solve for x
    x = 676,893.46/686.05
  6. Step 6: Final answer
    x = 986.66

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Why These Related Problems?

These problems maintain the same ratio (1.20) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.