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Finding the Third Proportional to 213.50 and 467.50

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Solution

The third proportional to 213.50 and 467.50 is: 1,023.68

Step by Step Solution

  1. Step 1: Write the proportion equation
    213.50 : 467.50 = 467.50 : x
  2. Step 2: Convert to fraction form
    213.50/467.50 = 467.50/x
  3. Step 3: Cross multiply
    213.50x = 467.50 × 467.50
  4. Step 4: Simplify right side
    213.50x = 218,556.25
  5. Step 5: Solve for x
    x = 218,556.25/213.50
  6. Step 6: Final answer
    x = 1,023.68

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Why These Related Problems?

These problems maintain the same ratio (2.19) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.