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Finding the Third Proportional to 97,406 and 209,986

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Solution

The third proportional to 97,406 and 209,986 is: 452,683.82

Step by Step Solution

  1. Step 1: Write the proportion equation
    97,406 : 209,986 = 209,986 : x
  2. Step 2: Convert to fraction form
    97,406/209,986 = 209,986/x
  3. Step 3: Cross multiply
    97,406x = 209,986 × 209,986
  4. Step 4: Simplify right side
    97,406x = 44,094,120,196
  5. Step 5: Solve for x
    x = 44,094,120,196/97,406
  6. Step 6: Final answer
    x = 452,683.82

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Why These Related Problems?

These problems maintain the same ratio (2.16) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.