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Finding the Third Proportional to 106,475 and 232,822

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Solution

The third proportional to 106,475 and 232,822 is: 509,096.82

Step by Step Solution

  1. Step 1: Write the proportion equation
    106,475 : 232,822 = 232,822 : x
  2. Step 2: Convert to fraction form
    106,475/232,822 = 232,822/x
  3. Step 3: Cross multiply
    106,475x = 232,822 × 232,822
  4. Step 4: Simplify right side
    106,475x = 54,206,083,684
  5. Step 5: Solve for x
    x = 54,206,083,684/106,475
  6. Step 6: Final answer
    x = 509,096.82

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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.