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Finding the Third Proportional to 7,826 and 17,416

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Solution

The third proportional to 7,826 and 17,416 is: 38,757.61

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,826 : 17,416 = 17,416 : x
  2. Step 2: Convert to fraction form
    7,826/17,416 = 17,416/x
  3. Step 3: Cross multiply
    7,826x = 17,416 × 17,416
  4. Step 4: Simplify right side
    7,826x = 303,317,056
  5. Step 5: Solve for x
    x = 303,317,056/7,826
  6. Step 6: Final answer
    x = 38,757.61

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Why These Related Problems?

These problems maintain the same ratio (2.23) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.