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Finding the Third Proportional to 197,696 and 411,776

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Solution

The third proportional to 197,696 and 411,776 is: 857,677.82

Step by Step Solution

  1. Step 1: Write the proportion equation
    197,696 : 411,776 = 411,776 : x
  2. Step 2: Convert to fraction form
    197,696/411,776 = 411,776/x
  3. Step 3: Cross multiply
    197,696x = 411,776 × 411,776
  4. Step 4: Simplify right side
    197,696x = 169,559,474,176
  5. Step 5: Solve for x
    x = 169,559,474,176/197,696
  6. Step 6: Final answer
    x = 857,677.82

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Why These Related Problems?

These problems maintain the same ratio (2.08) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.