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Finding the Third Proportional to 106,523 and 232,114

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Solution

The third proportional to 106,523 and 232,114 is: 505,777.24

Step by Step Solution

  1. Step 1: Write the proportion equation
    106,523 : 232,114 = 232,114 : x
  2. Step 2: Convert to fraction form
    106,523/232,114 = 232,114/x
  3. Step 3: Cross multiply
    106,523x = 232,114 × 232,114
  4. Step 4: Simplify right side
    106,523x = 53,876,908,996
  5. Step 5: Solve for x
    x = 53,876,908,996/106,523
  6. Step 6: Final answer
    x = 505,777.24

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Why These Related Problems?

These problems maintain the same ratio (2.18) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.