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Finding the Third Proportional to 217.75 and 509.50

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Solution

The third proportional to 217.75 and 509.50 is: 1,192.15

Step by Step Solution

  1. Step 1: Write the proportion equation
    217.75 : 509.50 = 509.50 : x
  2. Step 2: Convert to fraction form
    217.75/509.50 = 509.50/x
  3. Step 3: Cross multiply
    217.75x = 509.50 × 509.50
  4. Step 4: Simplify right side
    217.75x = 259,590.25
  5. Step 5: Solve for x
    x = 259,590.25/217.75
  6. Step 6: Final answer
    x = 1,192.15

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Why These Related Problems?

These problems maintain the same ratio (2.34) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.