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Finding the Third Proportional to 17,742 and 38,406

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Solution

The third proportional to 17,742 and 38,406 is: 83,137.24

Step by Step Solution

  1. Step 1: Write the proportion equation
    17,742 : 38,406 = 38,406 : x
  2. Step 2: Convert to fraction form
    17,742/38,406 = 38,406/x
  3. Step 3: Cross multiply
    17,742x = 38,406 × 38,406
  4. Step 4: Simplify right side
    17,742x = 1,475,020,836
  5. Step 5: Solve for x
    x = 1,475,020,836/17,742
  6. Step 6: Final answer
    x = 83,137.24

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Why These Related Problems?

These problems maintain the same ratio (2.16) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.