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Finding the Third Proportional to 205 and 314

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Solution

The third proportional to 205 and 314 is: 480.96

Step by Step Solution

  1. Step 1: Write the proportion equation
    205 : 314 = 314 : x
  2. Step 2: Convert to fraction form
    205/314 = 314/x
  3. Step 3: Cross multiply
    205x = 314 × 314
  4. Step 4: Simplify right side
    205x = 98,596
  5. Step 5: Solve for x
    x = 98,596/205
  6. Step 6: Final answer
    x = 480.96

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