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Finding the Third Proportional to 4,162 and 5,854

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Solution

The third proportional to 4,162 and 5,854 is: 8,233.86

Step by Step Solution

  1. Step 1: Write the proportion equation
    4,162 : 5,854 = 5,854 : x
  2. Step 2: Convert to fraction form
    4,162/5,854 = 5,854/x
  3. Step 3: Cross multiply
    4,162x = 5,854 × 5,854
  4. Step 4: Simplify right side
    4,162x = 34,269,316
  5. Step 5: Solve for x
    x = 34,269,316/4,162
  6. Step 6: Final answer
    x = 8,233.86

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Why These Related Problems?

These problems maintain the same ratio (1.41) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.