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Finding the Third Proportional to 5,186 and 8,259

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Solution

The third proportional to 5,186 and 8,259 is: 13,152.93

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,186 : 8,259 = 8,259 : x
  2. Step 2: Convert to fraction form
    5,186/8,259 = 8,259/x
  3. Step 3: Cross multiply
    5,186x = 8,259 × 8,259
  4. Step 4: Simplify right side
    5,186x = 68,211,081
  5. Step 5: Solve for x
    x = 68,211,081/5,186
  6. Step 6: Final answer
    x = 13,152.93

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Why These Related Problems?

These problems maintain the same ratio (1.59) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.