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Finding the Third Proportional to 180,960 and 378,416

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Solution

The third proportional to 180,960 and 378,416 is: 791,327.75

Step by Step Solution

  1. Step 1: Write the proportion equation
    180,960 : 378,416 = 378,416 : x
  2. Step 2: Convert to fraction form
    180,960/378,416 = 378,416/x
  3. Step 3: Cross multiply
    180,960x = 378,416 × 378,416
  4. Step 4: Simplify right side
    180,960x = 143,198,669,056
  5. Step 5: Solve for x
    x = 143,198,669,056/180,960
  6. Step 6: Final answer
    x = 791,327.75

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Why These Related Problems?

These problems maintain the same ratio (2.09) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.