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Finding the Third Proportional to 12,024 and 15,642

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Solution

The third proportional to 12,024 and 15,642 is: 20,348.65

Step by Step Solution

  1. Step 1: Write the proportion equation
    12,024 : 15,642 = 15,642 : x
  2. Step 2: Convert to fraction form
    12,024/15,642 = 15,642/x
  3. Step 3: Cross multiply
    12,024x = 15,642 × 15,642
  4. Step 4: Simplify right side
    12,024x = 244,672,164
  5. Step 5: Solve for x
    x = 244,672,164/12,024
  6. Step 6: Final answer
    x = 20,348.65

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Why These Related Problems?

These problems maintain the same ratio (1.30) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.