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Finding the Third Proportional to 209 and 306

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Solution

The third proportional to 209 and 306 is: 448.02

Step by Step Solution

  1. Step 1: Write the proportion equation
    209 : 306 = 306 : x
  2. Step 2: Convert to fraction form
    209/306 = 306/x
  3. Step 3: Cross multiply
    209x = 306 × 306
  4. Step 4: Simplify right side
    209x = 93,636
  5. Step 5: Solve for x
    x = 93,636/209
  6. Step 6: Final answer
    x = 448.02

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Why These Related Problems?

These problems maintain the same ratio (1.46) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.