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Finding the Third Proportional to 213 and 414.75

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Solution

The third proportional to 213 and 414.75 is: 807.59

Step by Step Solution

  1. Step 1: Write the proportion equation
    213 : 414.75 = 414.75 : x
  2. Step 2: Convert to fraction form
    213/414.75 = 414.75/x
  3. Step 3: Cross multiply
    213x = 414.75 × 414.75
  4. Step 4: Simplify right side
    213x = 172,017.56
  5. Step 5: Solve for x
    x = 172,017.56/213
  6. Step 6: Final answer
    x = 807.59

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Why These Related Problems?

These problems maintain the same ratio (1.95) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.