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Finding the Third Proportional to 97,834 and 214,424

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Solution

The third proportional to 97,834 and 214,424 is: 469,955.76

Step by Step Solution

  1. Step 1: Write the proportion equation
    97,834 : 214,424 = 214,424 : x
  2. Step 2: Convert to fraction form
    97,834/214,424 = 214,424/x
  3. Step 3: Cross multiply
    97,834x = 214,424 × 214,424
  4. Step 4: Simplify right side
    97,834x = 45,977,651,776
  5. Step 5: Solve for x
    x = 45,977,651,776/97,834
  6. Step 6: Final answer
    x = 469,955.76

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Why These Related Problems?

These problems maintain the same ratio (2.19) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.