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Finding the Third Proportional to 106,085 and 231,106

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Solution

The third proportional to 106,085 and 231,106 is: 503,464.05

Step by Step Solution

  1. Step 1: Write the proportion equation
    106,085 : 231,106 = 231,106 : x
  2. Step 2: Convert to fraction form
    106,085/231,106 = 231,106/x
  3. Step 3: Cross multiply
    106,085x = 231,106 × 231,106
  4. Step 4: Simplify right side
    106,085x = 53,409,983,236
  5. Step 5: Solve for x
    x = 53,409,983,236/106,085
  6. Step 6: Final answer
    x = 503,464.05

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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.