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Finding the Third Proportional to 65,106 and 133,284

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Solution

The third proportional to 65,106 and 133,284 is: 272,856.95

Step by Step Solution

  1. Step 1: Write the proportion equation
    65,106 : 133,284 = 133,284 : x
  2. Step 2: Convert to fraction form
    65,106/133,284 = 133,284/x
  3. Step 3: Cross multiply
    65,106x = 133,284 × 133,284
  4. Step 4: Simplify right side
    65,106x = 17,764,624,656
  5. Step 5: Solve for x
    x = 17,764,624,656/65,106
  6. Step 6: Final answer
    x = 272,856.95

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Why These Related Problems?

These problems maintain the same ratio (2.05) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.