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Finding the Third Proportional to 105,984 and 232,864

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Solution

The third proportional to 105,984 and 232,864 is: 511,639.89

Step by Step Solution

  1. Step 1: Write the proportion equation
    105,984 : 232,864 = 232,864 : x
  2. Step 2: Convert to fraction form
    105,984/232,864 = 232,864/x
  3. Step 3: Cross multiply
    105,984x = 232,864 × 232,864
  4. Step 4: Simplify right side
    105,984x = 54,225,642,496
  5. Step 5: Solve for x
    x = 54,225,642,496/105,984
  6. Step 6: Final answer
    x = 511,639.89

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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.