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Finding the Third Proportional to 199,038 and 416,514

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Solution

The third proportional to 199,038 and 416,514 is: 871,612.01

Step by Step Solution

  1. Step 1: Write the proportion equation
    199,038 : 416,514 = 416,514 : x
  2. Step 2: Convert to fraction form
    199,038/416,514 = 416,514/x
  3. Step 3: Cross multiply
    199,038x = 416,514 × 416,514
  4. Step 4: Simplify right side
    199,038x = 173,483,912,196
  5. Step 5: Solve for x
    x = 173,483,912,196/199,038
  6. Step 6: Final answer
    x = 871,612.01

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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.