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Finding the Third Proportional to 65,536 and 100,214

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Solution

The third proportional to 65,536 and 100,214 is: 153,241.67

Step by Step Solution

  1. Step 1: Write the proportion equation
    65,536 : 100,214 = 100,214 : x
  2. Step 2: Convert to fraction form
    65,536/100,214 = 100,214/x
  3. Step 3: Cross multiply
    65,536x = 100,214 × 100,214
  4. Step 4: Simplify right side
    65,536x = 10,042,845,796
  5. Step 5: Solve for x
    x = 10,042,845,796/65,536
  6. Step 6: Final answer
    x = 153,241.67

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Why These Related Problems?

These problems maintain the same ratio (1.53) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.