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Finding the Third Proportional to 417.23 and 567.84

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Solution

The third proportional to 417.23 and 567.84 is: 772.82

Step by Step Solution

  1. Step 1: Write the proportion equation
    417.23 : 567.84 = 567.84 : x
  2. Step 2: Convert to fraction form
    417.23/567.84 = 567.84/x
  3. Step 3: Cross multiply
    417.23x = 567.84 × 567.84
  4. Step 4: Simplify right side
    417.23x = 322,446.52
  5. Step 5: Solve for x
    x = 322,446.52/417.23
  6. Step 6: Final answer
    x = 772.82

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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.