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Finding the Third Proportional to 199,009 and 416,466

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Solution

The third proportional to 199,009 and 416,466 is: 871,538.12

Step by Step Solution

  1. Step 1: Write the proportion equation
    199,009 : 416,466 = 416,466 : x
  2. Step 2: Convert to fraction form
    199,009/416,466 = 416,466/x
  3. Step 3: Cross multiply
    199,009x = 416,466 × 416,466
  4. Step 4: Simplify right side
    199,009x = 173,443,929,156
  5. Step 5: Solve for x
    x = 173,443,929,156/199,009
  6. Step 6: Final answer
    x = 871,538.12

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Why These Related Problems?

These problems maintain the same ratio (2.09) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.