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Finding the Third Proportional to 8,462 and 12,416

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Solution

The third proportional to 8,462 and 12,416 is: 18,217.57

Step by Step Solution

  1. Step 1: Write the proportion equation
    8,462 : 12,416 = 12,416 : x
  2. Step 2: Convert to fraction form
    8,462/12,416 = 12,416/x
  3. Step 3: Cross multiply
    8,462x = 12,416 × 12,416
  4. Step 4: Simplify right side
    8,462x = 154,157,056
  5. Step 5: Solve for x
    x = 154,157,056/8,462
  6. Step 6: Final answer
    x = 18,217.57

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Why These Related Problems?

These problems maintain the same ratio (1.47) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.