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Finding the Third Proportional to 10,197 and 15,677

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Solution

The third proportional to 10,197 and 15,677 is: 24,102.02

Step by Step Solution

  1. Step 1: Write the proportion equation
    10,197 : 15,677 = 15,677 : x
  2. Step 2: Convert to fraction form
    10,197/15,677 = 15,677/x
  3. Step 3: Cross multiply
    10,197x = 15,677 × 15,677
  4. Step 4: Simplify right side
    10,197x = 245,768,329
  5. Step 5: Solve for x
    x = 245,768,329/10,197
  6. Step 6: Final answer
    x = 24,102.02

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Why These Related Problems?

These problems maintain the same ratio (1.54) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.