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Finding the Third Proportional to 105,970 and 230,165

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Solution

The third proportional to 105,970 and 230,165 is: 499,914.38

Step by Step Solution

  1. Step 1: Write the proportion equation
    105,970 : 230,165 = 230,165 : x
  2. Step 2: Convert to fraction form
    105,970/230,165 = 230,165/x
  3. Step 3: Cross multiply
    105,970x = 230,165 × 230,165
  4. Step 4: Simplify right side
    105,970x = 52,975,927,225
  5. Step 5: Solve for x
    x = 52,975,927,225/105,970
  6. Step 6: Final answer
    x = 499,914.38

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Why These Related Problems?

These problems maintain the same ratio (2.17) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.