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Finding the Third Proportional to 7,830 and 10,857

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Solution

The third proportional to 7,830 and 10,857 is: 15,054.21

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,830 : 10,857 = 10,857 : x
  2. Step 2: Convert to fraction form
    7,830/10,857 = 10,857/x
  3. Step 3: Cross multiply
    7,830x = 10,857 × 10,857
  4. Step 4: Simplify right side
    7,830x = 117,874,449
  5. Step 5: Solve for x
    x = 117,874,449/7,830
  6. Step 6: Final answer
    x = 15,054.21

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Why These Related Problems?

These problems maintain the same ratio (1.39) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.