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Finding the Third Proportional to 105,650 and 229,214

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Solution

The third proportional to 105,650 and 229,214 is: 497,293.50

Step by Step Solution

  1. Step 1: Write the proportion equation
    105,650 : 229,214 = 229,214 : x
  2. Step 2: Convert to fraction form
    105,650/229,214 = 229,214/x
  3. Step 3: Cross multiply
    105,650x = 229,214 × 229,214
  4. Step 4: Simplify right side
    105,650x = 52,539,057,796
  5. Step 5: Solve for x
    x = 52,539,057,796/105,650
  6. Step 6: Final answer
    x = 497,293.50

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Why These Related Problems?

These problems maintain the same ratio (2.17) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.