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Finding the Third Proportional to 233,729 and 511,684

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Solution

The third proportional to 233,729 and 511,684 is: 1,120,188.41

Step by Step Solution

  1. Step 1: Write the proportion equation
    233,729 : 511,684 = 511,684 : x
  2. Step 2: Convert to fraction form
    233,729/511,684 = 511,684/x
  3. Step 3: Cross multiply
    233,729x = 511,684 × 511,684
  4. Step 4: Simplify right side
    233,729x = 261,820,515,856
  5. Step 5: Solve for x
    x = 261,820,515,856/233,729
  6. Step 6: Final answer
    x = 1,120,188.41

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Why These Related Problems?

These problems maintain the same ratio (2.19) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.