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Finding the Third Proportional to 197,697 and 411,778

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Solution

The third proportional to 197,697 and 411,778 is: 857,681.81

Step by Step Solution

  1. Step 1: Write the proportion equation
    197,697 : 411,778 = 411,778 : x
  2. Step 2: Convert to fraction form
    197,697/411,778 = 411,778/x
  3. Step 3: Cross multiply
    197,697x = 411,778 × 411,778
  4. Step 4: Simplify right side
    197,697x = 169,561,121,284
  5. Step 5: Solve for x
    x = 169,561,121,284/197,697
  6. Step 6: Final answer
    x = 857,681.81

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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.