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Finding the Third Proportional to 213 and 415.38

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Solution

The third proportional to 213 and 415.38 is: 810.03

Step by Step Solution

  1. Step 1: Write the proportion equation
    213 : 415.38 = 415.38 : x
  2. Step 2: Convert to fraction form
    213/415.38 = 415.38/x
  3. Step 3: Cross multiply
    213x = 415.38 × 415.38
  4. Step 4: Simplify right side
    213x = 172,536.39
  5. Step 5: Solve for x
    x = 172,536.39/213
  6. Step 6: Final answer
    x = 810.03

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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.