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Finding the Third Proportional to 81,776 and 176,448

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Solution

The third proportional to 81,776 and 176,448 is: 380,721.69

Step by Step Solution

  1. Step 1: Write the proportion equation
    81,776 : 176,448 = 176,448 : x
  2. Step 2: Convert to fraction form
    81,776/176,448 = 176,448/x
  3. Step 3: Cross multiply
    81,776x = 176,448 × 176,448
  4. Step 4: Simplify right side
    81,776x = 31,133,896,704
  5. Step 5: Solve for x
    x = 31,133,896,704/81,776
  6. Step 6: Final answer
    x = 380,721.69

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Why These Related Problems?

These problems maintain the same ratio (2.16) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.