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Finding the Third Proportional to 106,971 and 229,123

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Solution

The third proportional to 106,971 and 229,123 is: 490,762.44

Step by Step Solution

  1. Step 1: Write the proportion equation
    106,971 : 229,123 = 229,123 : x
  2. Step 2: Convert to fraction form
    106,971/229,123 = 229,123/x
  3. Step 3: Cross multiply
    106,971x = 229,123 × 229,123
  4. Step 4: Simplify right side
    106,971x = 52,497,349,129
  5. Step 5: Solve for x
    x = 52,497,349,129/106,971
  6. Step 6: Final answer
    x = 490,762.44

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Why These Related Problems?

These problems maintain the same ratio (2.14) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.