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Finding the Third Proportional to 7,406 and 8,144

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Solution

The third proportional to 7,406 and 8,144 is: 8,955.54

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,406 : 8,144 = 8,144 : x
  2. Step 2: Convert to fraction form
    7,406/8,144 = 8,144/x
  3. Step 3: Cross multiply
    7,406x = 8,144 × 8,144
  4. Step 4: Simplify right side
    7,406x = 66,324,736
  5. Step 5: Solve for x
    x = 66,324,736/7,406
  6. Step 6: Final answer
    x = 8,955.54

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Why These Related Problems?

These problems maintain the same ratio (1.10) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.