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Finding the Third Proportional to 12,314 and 18,416

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Solution

The third proportional to 12,314 and 18,416 is: 27,541.75

Step by Step Solution

  1. Step 1: Write the proportion equation
    12,314 : 18,416 = 18,416 : x
  2. Step 2: Convert to fraction form
    12,314/18,416 = 18,416/x
  3. Step 3: Cross multiply
    12,314x = 18,416 × 18,416
  4. Step 4: Simplify right side
    12,314x = 339,149,056
  5. Step 5: Solve for x
    x = 339,149,056/12,314
  6. Step 6: Final answer
    x = 27,541.75

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.