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Finding the Third Proportional to 13,842 and 16,434

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Solution

The third proportional to 13,842 and 16,434 is: 19,511.37

Step by Step Solution

  1. Step 1: Write the proportion equation
    13,842 : 16,434 = 16,434 : x
  2. Step 2: Convert to fraction form
    13,842/16,434 = 16,434/x
  3. Step 3: Cross multiply
    13,842x = 16,434 × 16,434
  4. Step 4: Simplify right side
    13,842x = 270,076,356
  5. Step 5: Solve for x
    x = 270,076,356/13,842
  6. Step 6: Final answer
    x = 19,511.37

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Why These Related Problems?

These problems maintain the same ratio (1.19) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.