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Finding the Third Proportional to 417.09 and 522.84

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Solution

The third proportional to 417.09 and 522.84 is: 655.41

Step by Step Solution

  1. Step 1: Write the proportion equation
    417.09 : 522.84 = 522.84 : x
  2. Step 2: Convert to fraction form
    417.09/522.84 = 522.84/x
  3. Step 3: Cross multiply
    417.09x = 522.84 × 522.84
  4. Step 4: Simplify right side
    417.09x = 273,365.59
  5. Step 5: Solve for x
    x = 273,365.59/417.09
  6. Step 6: Final answer
    x = 655.41

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Why These Related Problems?

These problems maintain the same ratio (1.25) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.