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Finding the Third Proportional to 415 and 785

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Solution

The third proportional to 415 and 785 is: 1,484.88

Step by Step Solution

  1. Step 1: Write the proportion equation
    415 : 785 = 785 : x
  2. Step 2: Convert to fraction form
    415/785 = 785/x
  3. Step 3: Cross multiply
    415x = 785 × 785
  4. Step 4: Simplify right side
    415x = 616,225
  5. Step 5: Solve for x
    x = 616,225/415
  6. Step 6: Final answer
    x = 1,484.88

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Why These Related Problems?

These problems maintain the same ratio (1.89) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.