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Finding the Third Proportional to 4,196 and 5,782

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Solution

The third proportional to 4,196 and 5,782 is: 7,967.47

Step by Step Solution

  1. Step 1: Write the proportion equation
    4,196 : 5,782 = 5,782 : x
  2. Step 2: Convert to fraction form
    4,196/5,782 = 5,782/x
  3. Step 3: Cross multiply
    4,196x = 5,782 × 5,782
  4. Step 4: Simplify right side
    4,196x = 33,431,524
  5. Step 5: Solve for x
    x = 33,431,524/4,196
  6. Step 6: Final answer
    x = 7,967.47

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Why These Related Problems?

These problems maintain the same ratio (1.38) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.