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Finding the Third Proportional to 83,098 and 177,854

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Solution

The third proportional to 83,098 and 177,854 is: 380,659.53

Step by Step Solution

  1. Step 1: Write the proportion equation
    83,098 : 177,854 = 177,854 : x
  2. Step 2: Convert to fraction form
    83,098/177,854 = 177,854/x
  3. Step 3: Cross multiply
    83,098x = 177,854 × 177,854
  4. Step 4: Simplify right side
    83,098x = 31,632,045,316
  5. Step 5: Solve for x
    x = 31,632,045,316/83,098
  6. Step 6: Final answer
    x = 380,659.53

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Why These Related Problems?

These problems maintain the same ratio (2.14) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.