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Finding the Third Proportional to 12,288 and 14,464

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Solution

The third proportional to 12,288 and 14,464 is: 17,025.33

Step by Step Solution

  1. Step 1: Write the proportion equation
    12,288 : 14,464 = 14,464 : x
  2. Step 2: Convert to fraction form
    12,288/14,464 = 14,464/x
  3. Step 3: Cross multiply
    12,288x = 14,464 × 14,464
  4. Step 4: Simplify right side
    12,288x = 209,207,296
  5. Step 5: Solve for x
    x = 209,207,296/12,288
  6. Step 6: Final answer
    x = 17,025.33

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Why These Related Problems?

These problems maintain the same ratio (1.18) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.