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Finding the Third Proportional to 10,234 and 14,082

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Solution

The third proportional to 10,234 and 14,082 is: 19,376.85

Step by Step Solution

  1. Step 1: Write the proportion equation
    10,234 : 14,082 = 14,082 : x
  2. Step 2: Convert to fraction form
    10,234/14,082 = 14,082/x
  3. Step 3: Cross multiply
    10,234x = 14,082 × 14,082
  4. Step 4: Simplify right side
    10,234x = 198,302,724
  5. Step 5: Solve for x
    x = 198,302,724/10,234
  6. Step 6: Final answer
    x = 19,376.85

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Why These Related Problems?

These problems maintain the same ratio (1.38) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.