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Finding the Third Proportional to 37,822 and 82,278

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Solution

The third proportional to 37,822 and 82,278 is: 178,987.61

Step by Step Solution

  1. Step 1: Write the proportion equation
    37,822 : 82,278 = 82,278 : x
  2. Step 2: Convert to fraction form
    37,822/82,278 = 82,278/x
  3. Step 3: Cross multiply
    37,822x = 82,278 × 82,278
  4. Step 4: Simplify right side
    37,822x = 6,769,669,284
  5. Step 5: Solve for x
    x = 6,769,669,284/37,822
  6. Step 6: Final answer
    x = 178,987.61

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Why These Related Problems?

These problems maintain the same ratio (2.18) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.