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Finding the Third Proportional to 12,538 and 19,524

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Solution

The third proportional to 12,538 and 19,524 is: 30,402.50

Step by Step Solution

  1. Step 1: Write the proportion equation
    12,538 : 19,524 = 19,524 : x
  2. Step 2: Convert to fraction form
    12,538/19,524 = 19,524/x
  3. Step 3: Cross multiply
    12,538x = 19,524 × 19,524
  4. Step 4: Simplify right side
    12,538x = 381,186,576
  5. Step 5: Solve for x
    x = 381,186,576/12,538
  6. Step 6: Final answer
    x = 30,402.50

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Why These Related Problems?

These problems maintain the same ratio (1.56) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.