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Finding the Third Proportional to 197,757 and 409,534

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Solution

The third proportional to 197,757 and 409,534 is: 848,101.95

Step by Step Solution

  1. Step 1: Write the proportion equation
    197,757 : 409,534 = 409,534 : x
  2. Step 2: Convert to fraction form
    197,757/409,534 = 409,534/x
  3. Step 3: Cross multiply
    197,757x = 409,534 × 409,534
  4. Step 4: Simplify right side
    197,757x = 167,718,097,156
  5. Step 5: Solve for x
    x = 167,718,097,156/197,757
  6. Step 6: Final answer
    x = 848,101.95

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Why These Related Problems?

These problems maintain the same ratio (2.07) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.