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Finding the Third Proportional to 198,413 and 416,483

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Solution

The third proportional to 198,413 and 416,483 is: 874,227.44

Step by Step Solution

  1. Step 1: Write the proportion equation
    198,413 : 416,483 = 416,483 : x
  2. Step 2: Convert to fraction form
    198,413/416,483 = 416,483/x
  3. Step 3: Cross multiply
    198,413x = 416,483 × 416,483
  4. Step 4: Simplify right side
    198,413x = 173,458,089,289
  5. Step 5: Solve for x
    x = 173,458,089,289/198,413
  6. Step 6: Final answer
    x = 874,227.44

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Why These Related Problems?

These problems maintain the same ratio (2.10) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.