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Finding the Third Proportional to 5,186 and 8,237

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Solution

The third proportional to 5,186 and 8,237 is: 13,082.95

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,186 : 8,237 = 8,237 : x
  2. Step 2: Convert to fraction form
    5,186/8,237 = 8,237/x
  3. Step 3: Cross multiply
    5,186x = 8,237 × 8,237
  4. Step 4: Simplify right side
    5,186x = 67,848,169
  5. Step 5: Solve for x
    x = 67,848,169/5,186
  6. Step 6: Final answer
    x = 13,082.95

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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.