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Finding the Third Proportional to 14,549 and 21,824

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Solution

The third proportional to 14,549 and 21,824 is: 32,736.75

Step by Step Solution

  1. Step 1: Write the proportion equation
    14,549 : 21,824 = 21,824 : x
  2. Step 2: Convert to fraction form
    14,549/21,824 = 21,824/x
  3. Step 3: Cross multiply
    14,549x = 21,824 × 21,824
  4. Step 4: Simplify right side
    14,549x = 476,286,976
  5. Step 5: Solve for x
    x = 476,286,976/14,549
  6. Step 6: Final answer
    x = 32,736.75

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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.