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Finding the Third Proportional to 3,489 and 5,416

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Solution

The third proportional to 3,489 and 5,416 is: 8,407.30

Step by Step Solution

  1. Step 1: Write the proportion equation
    3,489 : 5,416 = 5,416 : x
  2. Step 2: Convert to fraction form
    3,489/5,416 = 5,416/x
  3. Step 3: Cross multiply
    3,489x = 5,416 × 5,416
  4. Step 4: Simplify right side
    3,489x = 29,333,056
  5. Step 5: Solve for x
    x = 29,333,056/3,489
  6. Step 6: Final answer
    x = 8,407.30

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Why These Related Problems?

These problems maintain the same ratio (1.55) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.