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Finding the Third Proportional to 64,096 and 97,100

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Solution

The third proportional to 64,096 and 97,100 is: 147,098.26

Step by Step Solution

  1. Step 1: Write the proportion equation
    64,096 : 97,100 = 97,100 : x
  2. Step 2: Convert to fraction form
    64,096/97,100 = 97,100/x
  3. Step 3: Cross multiply
    64,096x = 97,100 × 97,100
  4. Step 4: Simplify right side
    64,096x = 9,428,410,000
  5. Step 5: Solve for x
    x = 9,428,410,000/64,096
  6. Step 6: Final answer
    x = 147,098.26

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Why These Related Problems?

These problems maintain the same ratio (1.51) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.