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Finding the Third Proportional to 209.75 and 321.50

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Solution

The third proportional to 209.75 and 321.50 is: 492.79

Step by Step Solution

  1. Step 1: Write the proportion equation
    209.75 : 321.50 = 321.50 : x
  2. Step 2: Convert to fraction form
    209.75/321.50 = 321.50/x
  3. Step 3: Cross multiply
    209.75x = 321.50 × 321.50
  4. Step 4: Simplify right side
    209.75x = 103,362.25
  5. Step 5: Solve for x
    x = 103,362.25/209.75
  6. Step 6: Final answer
    x = 492.79

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Why These Related Problems?

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