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Finding the Third Proportional to 85,705 and 188,021

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Solution

The third proportional to 85,705 and 188,021 is: 412,483.48

Step by Step Solution

  1. Step 1: Write the proportion equation
    85,705 : 188,021 = 188,021 : x
  2. Step 2: Convert to fraction form
    85,705/188,021 = 188,021/x
  3. Step 3: Cross multiply
    85,705x = 188,021 × 188,021
  4. Step 4: Simplify right side
    85,705x = 35,351,896,441
  5. Step 5: Solve for x
    x = 35,351,896,441/85,705
  6. Step 6: Final answer
    x = 412,483.48

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Why These Related Problems?

These problems maintain the same ratio (2.19) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.