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Finding the Third Proportional to 6,297 and 13,677

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Solution

The third proportional to 6,297 and 13,677 is: 29,706.26

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,297 : 13,677 = 13,677 : x
  2. Step 2: Convert to fraction form
    6,297/13,677 = 13,677/x
  3. Step 3: Cross multiply
    6,297x = 13,677 × 13,677
  4. Step 4: Simplify right side
    6,297x = 187,060,329
  5. Step 5: Solve for x
    x = 187,060,329/6,297
  6. Step 6: Final answer
    x = 29,706.26

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Why These Related Problems?

These problems maintain the same ratio (2.17) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.