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Finding the Third Proportional to 6,578 and 13,972

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Solution

The third proportional to 6,578 and 13,972 is: 29,677.22

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,578 : 13,972 = 13,972 : x
  2. Step 2: Convert to fraction form
    6,578/13,972 = 13,972/x
  3. Step 3: Cross multiply
    6,578x = 13,972 × 13,972
  4. Step 4: Simplify right side
    6,578x = 195,216,784
  5. Step 5: Solve for x
    x = 195,216,784/6,578
  6. Step 6: Final answer
    x = 29,677.22

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Why These Related Problems?

These problems maintain the same ratio (2.12) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.