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Finding the Third Proportional to 197,700 and 411,784

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Solution

The third proportional to 197,700 and 411,784 is: 857,693.79

Step by Step Solution

  1. Step 1: Write the proportion equation
    197,700 : 411,784 = 411,784 : x
  2. Step 2: Convert to fraction form
    197,700/411,784 = 411,784/x
  3. Step 3: Cross multiply
    197,700x = 411,784 × 411,784
  4. Step 4: Simplify right side
    197,700x = 169,566,062,656
  5. Step 5: Solve for x
    x = 169,566,062,656/197,700
  6. Step 6: Final answer
    x = 857,693.79

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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.