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Finding the Third Proportional to 105,972 and 232,859

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Solution

The third proportional to 105,972 and 232,859 is: 511,675.86

Step by Step Solution

  1. Step 1: Write the proportion equation
    105,972 : 232,859 = 232,859 : x
  2. Step 2: Convert to fraction form
    105,972/232,859 = 232,859/x
  3. Step 3: Cross multiply
    105,972x = 232,859 × 232,859
  4. Step 4: Simplify right side
    105,972x = 54,223,313,881
  5. Step 5: Solve for x
    x = 54,223,313,881/105,972
  6. Step 6: Final answer
    x = 511,675.86

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Why These Related Problems?

These problems maintain the same ratio (2.20) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.