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Finding the Third Proportional to 209.81 and 313.69

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Solution

The third proportional to 209.81 and 313.69 is: 468.99

Step by Step Solution

  1. Step 1: Write the proportion equation
    209.81 : 313.69 = 313.69 : x
  2. Step 2: Convert to fraction form
    209.81/313.69 = 313.69/x
  3. Step 3: Cross multiply
    209.81x = 313.69 × 313.69
  4. Step 4: Simplify right side
    209.81x = 98,399.85
  5. Step 5: Solve for x
    x = 98,399.85/209.81
  6. Step 6: Final answer
    x = 468.99

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These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.