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Finding the Third Proportional to 564.75 and 665.38

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Solution

The third proportional to 564.75 and 665.38 is: 783.93

Step by Step Solution

  1. Step 1: Write the proportion equation
    564.75 : 665.38 = 665.38 : x
  2. Step 2: Convert to fraction form
    564.75/665.38 = 665.38/x
  3. Step 3: Cross multiply
    564.75x = 665.38 × 665.38
  4. Step 4: Simplify right side
    564.75x = 442,723.89
  5. Step 5: Solve for x
    x = 442,723.89/564.75
  6. Step 6: Final answer
    x = 783.93

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Why These Related Problems?

These problems maintain the same ratio (1.18) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.