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Finding the Third Proportional to 97,659 and 214,014

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Solution

The third proportional to 97,659 and 214,014 is: 468,999.19

Step by Step Solution

  1. Step 1: Write the proportion equation
    97,659 : 214,014 = 214,014 : x
  2. Step 2: Convert to fraction form
    97,659/214,014 = 214,014/x
  3. Step 3: Cross multiply
    97,659x = 214,014 × 214,014
  4. Step 4: Simplify right side
    97,659x = 45,801,992,196
  5. Step 5: Solve for x
    x = 45,801,992,196/97,659
  6. Step 6: Final answer
    x = 468,999.19

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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.