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Finding the Third Proportional to 82,400 and 177,224

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Solution

The third proportional to 82,400 and 177,224 is: 381,169.25

Step by Step Solution

  1. Step 1: Write the proportion equation
    82,400 : 177,224 = 177,224 : x
  2. Step 2: Convert to fraction form
    82,400/177,224 = 177,224/x
  3. Step 3: Cross multiply
    82,400x = 177,224 × 177,224
  4. Step 4: Simplify right side
    82,400x = 31,408,346,176
  5. Step 5: Solve for x
    x = 31,408,346,176/82,400
  6. Step 6: Final answer
    x = 381,169.25

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Why These Related Problems?

These problems maintain the same ratio (2.15) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.