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Finding the Third Proportional to 213 and 417

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Solution

The third proportional to 213 and 417 is: 816.38

Step by Step Solution

  1. Step 1: Write the proportion equation
    213 : 417 = 417 : x
  2. Step 2: Convert to fraction form
    213/417 = 417/x
  3. Step 3: Cross multiply
    213x = 417 × 417
  4. Step 4: Simplify right side
    213x = 173,889
  5. Step 5: Solve for x
    x = 173,889/213
  6. Step 6: Final answer
    x = 816.38

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Why These Related Problems?

These problems maintain the same ratio (1.96) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.