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Finding the Third Proportional to 75,744 and 164,352

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Solution

The third proportional to 75,744 and 164,352 is: 356,616.76

Step by Step Solution

  1. Step 1: Write the proportion equation
    75,744 : 164,352 = 164,352 : x
  2. Step 2: Convert to fraction form
    75,744/164,352 = 164,352/x
  3. Step 3: Cross multiply
    75,744x = 164,352 × 164,352
  4. Step 4: Simplify right side
    75,744x = 27,011,579,904
  5. Step 5: Solve for x
    x = 27,011,579,904/75,744
  6. Step 6: Final answer
    x = 356,616.76

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Why These Related Problems?

These problems maintain the same ratio (2.17) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.