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Finding the Third Proportional to 5,164 and 7,856

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Solution

The third proportional to 5,164 and 7,856 is: 11,951.34

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,164 : 7,856 = 7,856 : x
  2. Step 2: Convert to fraction form
    5,164/7,856 = 7,856/x
  3. Step 3: Cross multiply
    5,164x = 7,856 × 7,856
  4. Step 4: Simplify right side
    5,164x = 61,716,736
  5. Step 5: Solve for x
    x = 61,716,736/5,164
  6. Step 6: Final answer
    x = 11,951.34

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Why These Related Problems?

These problems maintain the same ratio (1.52) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.