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Finding the Third Proportional to 30,397 and 65,834

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Solution

The third proportional to 30,397 and 65,834 is: 142,583.66

Step by Step Solution

  1. Step 1: Write the proportion equation
    30,397 : 65,834 = 65,834 : x
  2. Step 2: Convert to fraction form
    30,397/65,834 = 65,834/x
  3. Step 3: Cross multiply
    30,397x = 65,834 × 65,834
  4. Step 4: Simplify right side
    30,397x = 4,334,115,556
  5. Step 5: Solve for x
    x = 4,334,115,556/30,397
  6. Step 6: Final answer
    x = 142,583.66

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Why These Related Problems?

These problems maintain the same ratio (2.17) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.