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Finding the Third Proportional to 5,461 and 8,197

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Solution

The third proportional to 5,461 and 8,197 is: 12,303.76

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,461 : 8,197 = 8,197 : x
  2. Step 2: Convert to fraction form
    5,461/8,197 = 8,197/x
  3. Step 3: Cross multiply
    5,461x = 8,197 × 8,197
  4. Step 4: Simplify right side
    5,461x = 67,190,809
  5. Step 5: Solve for x
    x = 67,190,809/5,461
  6. Step 6: Final answer
    x = 12,303.76

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.