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Finding the Third Proportional to 233,784 and 511,306

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Solution

The third proportional to 233,784 and 511,306 is: 1,118,270.82

Step by Step Solution

  1. Step 1: Write the proportion equation
    233,784 : 511,306 = 511,306 : x
  2. Step 2: Convert to fraction form
    233,784/511,306 = 511,306/x
  3. Step 3: Cross multiply
    233,784x = 511,306 × 511,306
  4. Step 4: Simplify right side
    233,784x = 261,433,825,636
  5. Step 5: Solve for x
    x = 261,433,825,636/233,784
  6. Step 6: Final answer
    x = 1,118,270.82

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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.