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Finding the Third Proportional to 37,986 and 83,619

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Solution

The third proportional to 37,986 and 83,619 is: 184,071.43

Step by Step Solution

  1. Step 1: Write the proportion equation
    37,986 : 83,619 = 83,619 : x
  2. Step 2: Convert to fraction form
    37,986/83,619 = 83,619/x
  3. Step 3: Cross multiply
    37,986x = 83,619 × 83,619
  4. Step 4: Simplify right side
    37,986x = 6,992,137,161
  5. Step 5: Solve for x
    x = 6,992,137,161/37,986
  6. Step 6: Final answer
    x = 184,071.43

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Why These Related Problems?

These problems maintain the same ratio (2.20) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.