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Finding the Third Proportional to 4,212 and 7,857

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Solution

The third proportional to 4,212 and 7,857 is: 14,656.33

Step by Step Solution

  1. Step 1: Write the proportion equation
    4,212 : 7,857 = 7,857 : x
  2. Step 2: Convert to fraction form
    4,212/7,857 = 7,857/x
  3. Step 3: Cross multiply
    4,212x = 7,857 × 7,857
  4. Step 4: Simplify right side
    4,212x = 61,732,449
  5. Step 5: Solve for x
    x = 61,732,449/4,212
  6. Step 6: Final answer
    x = 14,656.33

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Why These Related Problems?

These problems maintain the same ratio (1.87) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.