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Finding the Third Proportional to 209 and 311.50

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Solution

The third proportional to 209 and 311.50 is: 464.27

Step by Step Solution

  1. Step 1: Write the proportion equation
    209 : 311.50 = 311.50 : x
  2. Step 2: Convert to fraction form
    209/311.50 = 311.50/x
  3. Step 3: Cross multiply
    209x = 311.50 × 311.50
  4. Step 4: Simplify right side
    209x = 97,032.25
  5. Step 5: Solve for x
    x = 97,032.25/209
  6. Step 6: Final answer
    x = 464.27

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Why These Related Problems?

These problems maintain the same ratio (1.49) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.