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Finding the Third Proportional to 6,114 and 6,906

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Solution

The third proportional to 6,114 and 6,906 is: 7,800.59

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,114 : 6,906 = 6,906 : x
  2. Step 2: Convert to fraction form
    6,114/6,906 = 6,906/x
  3. Step 3: Cross multiply
    6,114x = 6,906 × 6,906
  4. Step 4: Simplify right side
    6,114x = 47,692,836
  5. Step 5: Solve for x
    x = 47,692,836/6,114
  6. Step 6: Final answer
    x = 7,800.59

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Why These Related Problems?

These problems maintain the same ratio (1.13) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.