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Finding the Third Proportional to 83,460 and 185,586

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Solution

The third proportional to 83,460 and 185,586 is: 412,678.69

Step by Step Solution

  1. Step 1: Write the proportion equation
    83,460 : 185,586 = 185,586 : x
  2. Step 2: Convert to fraction form
    83,460/185,586 = 185,586/x
  3. Step 3: Cross multiply
    83,460x = 185,586 × 185,586
  4. Step 4: Simplify right side
    83,460x = 34,442,163,396
  5. Step 5: Solve for x
    x = 34,442,163,396/83,460
  6. Step 6: Final answer
    x = 412,678.69

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Why These Related Problems?

These problems maintain the same ratio (2.22) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.