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Finding the Third Proportional to 417.09 and 584.86

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Solution

The third proportional to 417.09 and 584.86 is: 820.10

Step by Step Solution

  1. Step 1: Write the proportion equation
    417.09 : 584.86 = 584.86 : x
  2. Step 2: Convert to fraction form
    417.09/584.86 = 584.86/x
  3. Step 3: Cross multiply
    417.09x = 584.86 × 584.86
  4. Step 4: Simplify right side
    417.09x = 342,060.49
  5. Step 5: Solve for x
    x = 342,060.49/417.09
  6. Step 6: Final answer
    x = 820.10

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Why These Related Problems?

These problems maintain the same ratio (1.40) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.