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Finding the Third Proportional to 205.45 and 342.14

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Solution

The third proportional to 205.45 and 342.14 is: 569.77

Step by Step Solution

  1. Step 1: Write the proportion equation
    205.45 : 342.14 = 342.14 : x
  2. Step 2: Convert to fraction form
    205.45/342.14 = 342.14/x
  3. Step 3: Cross multiply
    205.45x = 342.14 × 342.14
  4. Step 4: Simplify right side
    205.45x = 117,060.21
  5. Step 5: Solve for x
    x = 117,060.21/205.45
  6. Step 6: Final answer
    x = 569.77

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Why These Related Problems?

These problems maintain the same ratio (1.67) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.