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Finding the Third Proportional to 7,820 and 18,206

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Solution

The third proportional to 7,820 and 18,206 is: 42,385.99

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,820 : 18,206 = 18,206 : x
  2. Step 2: Convert to fraction form
    7,820/18,206 = 18,206/x
  3. Step 3: Cross multiply
    7,820x = 18,206 × 18,206
  4. Step 4: Simplify right side
    7,820x = 331,458,436
  5. Step 5: Solve for x
    x = 331,458,436/7,820
  6. Step 6: Final answer
    x = 42,385.99

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Why These Related Problems?

These problems maintain the same ratio (2.33) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.