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Finding the Third Proportional to 65,038 and 97,286

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Solution

The third proportional to 65,038 and 97,286 is: 145,523.63

Step by Step Solution

  1. Step 1: Write the proportion equation
    65,038 : 97,286 = 97,286 : x
  2. Step 2: Convert to fraction form
    65,038/97,286 = 97,286/x
  3. Step 3: Cross multiply
    65,038x = 97,286 × 97,286
  4. Step 4: Simplify right side
    65,038x = 9,464,565,796
  5. Step 5: Solve for x
    x = 9,464,565,796/65,038
  6. Step 6: Final answer
    x = 145,523.63

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.