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Finding the Third Proportional to 205,024 and 313,416

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Solution

The third proportional to 205,024 and 313,416 is: 479,112.64

Step by Step Solution

  1. Step 1: Write the proportion equation
    205,024 : 313,416 = 313,416 : x
  2. Step 2: Convert to fraction form
    205,024/313,416 = 313,416/x
  3. Step 3: Cross multiply
    205,024x = 313,416 × 313,416
  4. Step 4: Simplify right side
    205,024x = 98,229,589,056
  5. Step 5: Solve for x
    x = 98,229,589,056/205,024
  6. Step 6: Final answer
    x = 479,112.64

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Why These Related Problems?

These problems maintain the same ratio (1.53) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.