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Finding the Third Proportional to 7,830 and 17,727

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Solution

The third proportional to 7,830 and 17,727 is: 40,133.66

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,830 : 17,727 = 17,727 : x
  2. Step 2: Convert to fraction form
    7,830/17,727 = 17,727/x
  3. Step 3: Cross multiply
    7,830x = 17,727 × 17,727
  4. Step 4: Simplify right side
    7,830x = 314,246,529
  5. Step 5: Solve for x
    x = 314,246,529/7,830
  6. Step 6: Final answer
    x = 40,133.66

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Why These Related Problems?

These problems maintain the same ratio (2.26) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.