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Finding the Third Proportional to 82,416 and 176,520

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Solution

The third proportional to 82,416 and 176,520 is: 378,073.56

Step by Step Solution

  1. Step 1: Write the proportion equation
    82,416 : 176,520 = 176,520 : x
  2. Step 2: Convert to fraction form
    82,416/176,520 = 176,520/x
  3. Step 3: Cross multiply
    82,416x = 176,520 × 176,520
  4. Step 4: Simplify right side
    82,416x = 31,159,310,400
  5. Step 5: Solve for x
    x = 31,159,310,400/82,416
  6. Step 6: Final answer
    x = 378,073.56

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Why These Related Problems?

These problems maintain the same ratio (2.14) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.