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Finding the Third Proportional to 38,196 and 82,034

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Solution

The third proportional to 38,196 and 82,034 is: 176,185.39

Step by Step Solution

  1. Step 1: Write the proportion equation
    38,196 : 82,034 = 82,034 : x
  2. Step 2: Convert to fraction form
    38,196/82,034 = 82,034/x
  3. Step 3: Cross multiply
    38,196x = 82,034 × 82,034
  4. Step 4: Simplify right side
    38,196x = 6,729,577,156
  5. Step 5: Solve for x
    x = 6,729,577,156/38,196
  6. Step 6: Final answer
    x = 176,185.39

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Why These Related Problems?

These problems maintain the same ratio (2.15) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.