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Finding the Third Proportional to 213.19 and 464.69

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Solution

The third proportional to 213.19 and 464.69 is: 1,012.89

Step by Step Solution

  1. Step 1: Write the proportion equation
    213.19 : 464.69 = 464.69 : x
  2. Step 2: Convert to fraction form
    213.19/464.69 = 464.69/x
  3. Step 3: Cross multiply
    213.19x = 464.69 × 464.69
  4. Step 4: Simplify right side
    213.19x = 215,934.47
  5. Step 5: Solve for x
    x = 215,934.47/213.19
  6. Step 6: Final answer
    x = 1,012.89

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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.