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Finding the Third Proportional to 8,314 and 10,177

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Solution

The third proportional to 8,314 and 10,177 is: 12,457.46

Step by Step Solution

  1. Step 1: Write the proportion equation
    8,314 : 10,177 = 10,177 : x
  2. Step 2: Convert to fraction form
    8,314/10,177 = 10,177/x
  3. Step 3: Cross multiply
    8,314x = 10,177 × 10,177
  4. Step 4: Simplify right side
    8,314x = 103,571,329
  5. Step 5: Solve for x
    x = 103,571,329/8,314
  6. Step 6: Final answer
    x = 12,457.46

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Why These Related Problems?

These problems maintain the same ratio (1.22) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.