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Finding the Third Proportional to 3,780 and 8,202

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Solution

The third proportional to 3,780 and 8,202 is: 17,797.04

Step by Step Solution

  1. Step 1: Write the proportion equation
    3,780 : 8,202 = 8,202 : x
  2. Step 2: Convert to fraction form
    3,780/8,202 = 8,202/x
  3. Step 3: Cross multiply
    3,780x = 8,202 × 8,202
  4. Step 4: Simplify right side
    3,780x = 67,272,804
  5. Step 5: Solve for x
    x = 67,272,804/3,780
  6. Step 6: Final answer
    x = 17,797.04

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Why These Related Problems?

These problems maintain the same ratio (2.17) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.