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Finding the Third Proportional to 106,424 and 229,458

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Solution

The third proportional to 106,424 and 229,458 is: 494,728.39

Step by Step Solution

  1. Step 1: Write the proportion equation
    106,424 : 229,458 = 229,458 : x
  2. Step 2: Convert to fraction form
    106,424/229,458 = 229,458/x
  3. Step 3: Cross multiply
    106,424x = 229,458 × 229,458
  4. Step 4: Simplify right side
    106,424x = 52,650,973,764
  5. Step 5: Solve for x
    x = 52,650,973,764/106,424
  6. Step 6: Final answer
    x = 494,728.39

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Why These Related Problems?

These problems maintain the same ratio (2.16) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.