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Finding the Third Proportional to 75,196 and 178,144

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Solution

The third proportional to 75,196 and 178,144 is: 422,034.21

Step by Step Solution

  1. Step 1: Write the proportion equation
    75,196 : 178,144 = 178,144 : x
  2. Step 2: Convert to fraction form
    75,196/178,144 = 178,144/x
  3. Step 3: Cross multiply
    75,196x = 178,144 × 178,144
  4. Step 4: Simplify right side
    75,196x = 31,735,284,736
  5. Step 5: Solve for x
    x = 31,735,284,736/75,196
  6. Step 6: Final answer
    x = 422,034.21

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Why These Related Problems?

These problems maintain the same ratio (2.37) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.