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Finding the Third Proportional to 51,194 and 82,178

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Solution

The third proportional to 51,194 and 82,178 is: 131,914.36

Step by Step Solution

  1. Step 1: Write the proportion equation
    51,194 : 82,178 = 82,178 : x
  2. Step 2: Convert to fraction form
    51,194/82,178 = 82,178/x
  3. Step 3: Cross multiply
    51,194x = 82,178 × 82,178
  4. Step 4: Simplify right side
    51,194x = 6,753,223,684
  5. Step 5: Solve for x
    x = 6,753,223,684/51,194
  6. Step 6: Final answer
    x = 131,914.36

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Why These Related Problems?

These problems maintain the same ratio (1.61) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.