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Finding the Third Proportional to 209 and 313.50

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Solution

The third proportional to 209 and 313.50 is: 470.25

Step by Step Solution

  1. Step 1: Write the proportion equation
    209 : 313.50 = 313.50 : x
  2. Step 2: Convert to fraction form
    209/313.50 = 313.50/x
  3. Step 3: Cross multiply
    209x = 313.50 × 313.50
  4. Step 4: Simplify right side
    209x = 98,282.25
  5. Step 5: Solve for x
    x = 98,282.25/209
  6. Step 6: Final answer
    x = 470.25

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Why These Related Problems?

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