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Finding the Third Proportional to 9,702 and 14,538

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Solution

The third proportional to 9,702 and 14,538 is: 21,784.52

Step by Step Solution

  1. Step 1: Write the proportion equation
    9,702 : 14,538 = 14,538 : x
  2. Step 2: Convert to fraction form
    9,702/14,538 = 14,538/x
  3. Step 3: Cross multiply
    9,702x = 14,538 × 14,538
  4. Step 4: Simplify right side
    9,702x = 211,353,444
  5. Step 5: Solve for x
    x = 211,353,444/9,702
  6. Step 6: Final answer
    x = 21,784.52

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.