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Finding the Third Proportional to 194,411 and 463,671

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Solution

The third proportional to 194,411 and 463,671 is: 1,105,857.16

Step by Step Solution

  1. Step 1: Write the proportion equation
    194,411 : 463,671 = 463,671 : x
  2. Step 2: Convert to fraction form
    194,411/463,671 = 463,671/x
  3. Step 3: Cross multiply
    194,411x = 463,671 × 463,671
  4. Step 4: Simplify right side
    194,411x = 214,990,796,241
  5. Step 5: Solve for x
    x = 214,990,796,241/194,411
  6. Step 6: Final answer
    x = 1,105,857.16

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Why These Related Problems?

These problems maintain the same ratio (2.39) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.