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Finding the Third Proportional to 12,416 and 15,742

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Solution

The third proportional to 12,416 and 15,742 is: 19,958.97

Step by Step Solution

  1. Step 1: Write the proportion equation
    12,416 : 15,742 = 15,742 : x
  2. Step 2: Convert to fraction form
    12,416/15,742 = 15,742/x
  3. Step 3: Cross multiply
    12,416x = 15,742 × 15,742
  4. Step 4: Simplify right side
    12,416x = 247,810,564
  5. Step 5: Solve for x
    x = 247,810,564/12,416
  6. Step 6: Final answer
    x = 19,958.97

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Why These Related Problems?

These problems maintain the same ratio (1.27) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.