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Finding the Third Proportional to 65,012 and 97,096

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Solution

The third proportional to 65,012 and 97,096 is: 145,013.74

Step by Step Solution

  1. Step 1: Write the proportion equation
    65,012 : 97,096 = 97,096 : x
  2. Step 2: Convert to fraction form
    65,012/97,096 = 97,096/x
  3. Step 3: Cross multiply
    65,012x = 97,096 × 97,096
  4. Step 4: Simplify right side
    65,012x = 9,427,633,216
  5. Step 5: Solve for x
    x = 9,427,633,216/65,012
  6. Step 6: Final answer
    x = 145,013.74

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Why These Related Problems?

These problems maintain the same ratio (1.49) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.