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Finding the Third Proportional to 213.25 and 509.75

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Solution

The third proportional to 213.25 and 509.75 is: 1,218.50

Step by Step Solution

  1. Step 1: Write the proportion equation
    213.25 : 509.75 = 509.75 : x
  2. Step 2: Convert to fraction form
    213.25/509.75 = 509.75/x
  3. Step 3: Cross multiply
    213.25x = 509.75 × 509.75
  4. Step 4: Simplify right side
    213.25x = 259,845.06
  5. Step 5: Solve for x
    x = 259,845.06/213.25
  6. Step 6: Final answer
    x = 1,218.50

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Why These Related Problems?

These problems maintain the same ratio (2.39) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.