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Finding the Third Proportional to 97,321 and 209,834

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Solution

The third proportional to 97,321 and 209,834 is: 452,423.50

Step by Step Solution

  1. Step 1: Write the proportion equation
    97,321 : 209,834 = 209,834 : x
  2. Step 2: Convert to fraction form
    97,321/209,834 = 209,834/x
  3. Step 3: Cross multiply
    97,321x = 209,834 × 209,834
  4. Step 4: Simplify right side
    97,321x = 44,030,307,556
  5. Step 5: Solve for x
    x = 44,030,307,556/97,321
  6. Step 6: Final answer
    x = 452,423.50

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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.