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Finding the Third Proportional to 6,416 and 13,789

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Solution

The third proportional to 6,416 and 13,789 is: 29,634.74

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,416 : 13,789 = 13,789 : x
  2. Step 2: Convert to fraction form
    6,416/13,789 = 13,789/x
  3. Step 3: Cross multiply
    6,416x = 13,789 × 13,789
  4. Step 4: Simplify right side
    6,416x = 190,136,521
  5. Step 5: Solve for x
    x = 190,136,521/6,416
  6. Step 6: Final answer
    x = 29,634.74

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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.