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Finding the Third Proportional to 212.24 and 462.92

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Solution

The third proportional to 212.24 and 462.92 is: 1,009.69

Step by Step Solution

  1. Step 1: Write the proportion equation
    212.24 : 462.92 = 462.92 : x
  2. Step 2: Convert to fraction form
    212.24/462.92 = 462.92/x
  3. Step 3: Cross multiply
    212.24x = 462.92 × 462.92
  4. Step 4: Simplify right side
    212.24x = 214,296.89
  5. Step 5: Solve for x
    x = 214,296.89/212.24
  6. Step 6: Final answer
    x = 1,009.69

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Why These Related Problems?

These problems maintain the same ratio (2.18) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.