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Finding the Third Proportional to 5,206 and 8,141

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Solution

The third proportional to 5,206 and 8,141 is: 12,730.67

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,206 : 8,141 = 8,141 : x
  2. Step 2: Convert to fraction form
    5,206/8,141 = 8,141/x
  3. Step 3: Cross multiply
    5,206x = 8,141 × 8,141
  4. Step 4: Simplify right side
    5,206x = 66,275,881
  5. Step 5: Solve for x
    x = 66,275,881/5,206
  6. Step 6: Final answer
    x = 12,730.67

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Why These Related Problems?

These problems maintain the same ratio (1.56) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.