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Finding the Third Proportional to 82,023 and 178,275

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Solution

The third proportional to 82,023 and 178,275 is: 387,476.39

Step by Step Solution

  1. Step 1: Write the proportion equation
    82,023 : 178,275 = 178,275 : x
  2. Step 2: Convert to fraction form
    82,023/178,275 = 178,275/x
  3. Step 3: Cross multiply
    82,023x = 178,275 × 178,275
  4. Step 4: Simplify right side
    82,023x = 31,781,975,625
  5. Step 5: Solve for x
    x = 31,781,975,625/82,023
  6. Step 6: Final answer
    x = 387,476.39

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Why These Related Problems?

These problems maintain the same ratio (2.17) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.