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Finding the Third Proportional to 12,194 and 16,464

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Solution

The third proportional to 12,194 and 16,464 is: 22,229.24

Step by Step Solution

  1. Step 1: Write the proportion equation
    12,194 : 16,464 = 16,464 : x
  2. Step 2: Convert to fraction form
    12,194/16,464 = 16,464/x
  3. Step 3: Cross multiply
    12,194x = 16,464 × 16,464
  4. Step 4: Simplify right side
    12,194x = 271,063,296
  5. Step 5: Solve for x
    x = 271,063,296/12,194
  6. Step 6: Final answer
    x = 22,229.24

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Why These Related Problems?

These problems maintain the same ratio (1.35) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.