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Finding the Third Proportional to 686 and 1,478

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Solution

The third proportional to 686 and 1,478 is: 3,184.38

Step by Step Solution

  1. Step 1: Write the proportion equation
    686 : 1,478 = 1,478 : x
  2. Step 2: Convert to fraction form
    686/1,478 = 1,478/x
  3. Step 3: Cross multiply
    686x = 1,478 × 1,478
  4. Step 4: Simplify right side
    686x = 2,184,484
  5. Step 5: Solve for x
    x = 2,184,484/686
  6. Step 6: Final answer
    x = 3,184.38

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Why These Related Problems?

These problems maintain the same ratio (2.15) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.