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Finding the Third Proportional to 205.98 and 314.26

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Solution

The third proportional to 205.98 and 314.26 is: 479.47

Step by Step Solution

  1. Step 1: Write the proportion equation
    205.98 : 314.26 = 314.26 : x
  2. Step 2: Convert to fraction form
    205.98/314.26 = 314.26/x
  3. Step 3: Cross multiply
    205.98x = 314.26 × 314.26
  4. Step 4: Simplify right side
    205.98x = 98,760.43
  5. Step 5: Solve for x
    x = 98,760.43/205.98
  6. Step 6: Final answer
    x = 479.47

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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.