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Finding the Third Proportional to 415.69 and 478.13

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Solution

The third proportional to 415.69 and 478.13 is: 549.94

Step by Step Solution

  1. Step 1: Write the proportion equation
    415.69 : 478.13 = 478.13 : x
  2. Step 2: Convert to fraction form
    415.69/478.13 = 478.13/x
  3. Step 3: Cross multiply
    415.69x = 478.13 × 478.13
  4. Step 4: Simplify right side
    415.69x = 228,603.52
  5. Step 5: Solve for x
    x = 228,603.52/415.69
  6. Step 6: Final answer
    x = 549.94

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Why These Related Problems?

These problems maintain the same ratio (1.15) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.