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Finding the Third Proportional to 13,498 and 31,524

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Solution

The third proportional to 13,498 and 31,524 is: 73,622.95

Step by Step Solution

  1. Step 1: Write the proportion equation
    13,498 : 31,524 = 31,524 : x
  2. Step 2: Convert to fraction form
    13,498/31,524 = 31,524/x
  3. Step 3: Cross multiply
    13,498x = 31,524 × 31,524
  4. Step 4: Simplify right side
    13,498x = 993,762,576
  5. Step 5: Solve for x
    x = 993,762,576/13,498
  6. Step 6: Final answer
    x = 73,622.95

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Why These Related Problems?

These problems maintain the same ratio (2.34) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.