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Finding the Third Proportional to 97,839 and 206,178

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Solution

The third proportional to 97,839 and 206,178 is: 434,482.85

Step by Step Solution

  1. Step 1: Write the proportion equation
    97,839 : 206,178 = 206,178 : x
  2. Step 2: Convert to fraction form
    97,839/206,178 = 206,178/x
  3. Step 3: Cross multiply
    97,839x = 206,178 × 206,178
  4. Step 4: Simplify right side
    97,839x = 42,509,367,684
  5. Step 5: Solve for x
    x = 42,509,367,684/97,839
  6. Step 6: Final answer
    x = 434,482.85

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Why These Related Problems?

These problems maintain the same ratio (2.11) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.