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Finding the Third Proportional to 82,821 and 178,761

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Solution

The third proportional to 82,821 and 178,761 is: 385,838.07

Step by Step Solution

  1. Step 1: Write the proportion equation
    82,821 : 178,761 = 178,761 : x
  2. Step 2: Convert to fraction form
    82,821/178,761 = 178,761/x
  3. Step 3: Cross multiply
    82,821x = 178,761 × 178,761
  4. Step 4: Simplify right side
    82,821x = 31,955,495,121
  5. Step 5: Solve for x
    x = 31,955,495,121/82,821
  6. Step 6: Final answer
    x = 385,838.07

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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.