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Finding the Third Proportional to 6,534 and 14,031

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Solution

The third proportional to 6,534 and 14,031 is: 30,129.93

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,534 : 14,031 = 14,031 : x
  2. Step 2: Convert to fraction form
    6,534/14,031 = 14,031/x
  3. Step 3: Cross multiply
    6,534x = 14,031 × 14,031
  4. Step 4: Simplify right side
    6,534x = 196,868,961
  5. Step 5: Solve for x
    x = 196,868,961/6,534
  6. Step 6: Final answer
    x = 30,129.93

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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.