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Finding the Third Proportional to 83,214 and 172,329

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Solution

The third proportional to 83,214 and 172,329 is: 356,878.46

Step by Step Solution

  1. Step 1: Write the proportion equation
    83,214 : 172,329 = 172,329 : x
  2. Step 2: Convert to fraction form
    83,214/172,329 = 172,329/x
  3. Step 3: Cross multiply
    83,214x = 172,329 × 172,329
  4. Step 4: Simplify right side
    83,214x = 29,697,284,241
  5. Step 5: Solve for x
    x = 29,697,284,241/83,214
  6. Step 6: Final answer
    x = 356,878.46

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Why These Related Problems?

These problems maintain the same ratio (2.07) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.