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Finding the Third Proportional to 205.88 and 293.94

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Solution

The third proportional to 205.88 and 293.94 is: 419.67

Step by Step Solution

  1. Step 1: Write the proportion equation
    205.88 : 293.94 = 293.94 : x
  2. Step 2: Convert to fraction form
    205.88/293.94 = 293.94/x
  3. Step 3: Cross multiply
    205.88x = 293.94 × 293.94
  4. Step 4: Simplify right side
    205.88x = 86,399.25
  5. Step 5: Solve for x
    x = 86,399.25/205.88
  6. Step 6: Final answer
    x = 419.67

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Why These Related Problems?

These problems maintain the same ratio (1.43) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.