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Finding the Third Proportional to 564.75 and 769.78

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Solution

The third proportional to 564.75 and 769.78 is: 1,049.25

Step by Step Solution

  1. Step 1: Write the proportion equation
    564.75 : 769.78 = 769.78 : x
  2. Step 2: Convert to fraction form
    564.75/769.78 = 769.78/x
  3. Step 3: Cross multiply
    564.75x = 769.78 × 769.78
  4. Step 4: Simplify right side
    564.75x = 592,563.17
  5. Step 5: Solve for x
    x = 592,563.17/564.75
  6. Step 6: Final answer
    x = 1,049.25

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Why These Related Problems?

These problems maintain the same ratio (1.36) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.