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Finding the Third Proportional to 83,164 and 177,776

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Solution

The third proportional to 83,164 and 177,776 is: 380,023.88

Step by Step Solution

  1. Step 1: Write the proportion equation
    83,164 : 177,776 = 177,776 : x
  2. Step 2: Convert to fraction form
    83,164/177,776 = 177,776/x
  3. Step 3: Cross multiply
    83,164x = 177,776 × 177,776
  4. Step 4: Simplify right side
    83,164x = 31,604,306,176
  5. Step 5: Solve for x
    x = 31,604,306,176/83,164
  6. Step 6: Final answer
    x = 380,023.88

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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.