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Finding the Third Proportional to 106,411 and 230,534

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Solution

The third proportional to 106,411 and 230,534 is: 499,440.14

Step by Step Solution

  1. Step 1: Write the proportion equation
    106,411 : 230,534 = 230,534 : x
  2. Step 2: Convert to fraction form
    106,411/230,534 = 230,534/x
  3. Step 3: Cross multiply
    106,411x = 230,534 × 230,534
  4. Step 4: Simplify right side
    106,411x = 53,145,925,156
  5. Step 5: Solve for x
    x = 53,145,925,156/106,411
  6. Step 6: Final answer
    x = 499,440.14

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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.