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Finding the Third Proportional to 76,414 and 165,965

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Solution

The third proportional to 76,414 and 165,965 is: 360,462.50

Step by Step Solution

  1. Step 1: Write the proportion equation
    76,414 : 165,965 = 165,965 : x
  2. Step 2: Convert to fraction form
    76,414/165,965 = 165,965/x
  3. Step 3: Cross multiply
    76,414x = 165,965 × 165,965
  4. Step 4: Simplify right side
    76,414x = 27,544,381,225
  5. Step 5: Solve for x
    x = 27,544,381,225/76,414
  6. Step 6: Final answer
    x = 360,462.50

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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.