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Finding the Third Proportional to 413 and 834

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Solution

The third proportional to 413 and 834 is: 1,684.15

Step by Step Solution

  1. Step 1: Write the proportion equation
    413 : 834 = 834 : x
  2. Step 2: Convert to fraction form
    413/834 = 834/x
  3. Step 3: Cross multiply
    413x = 834 × 834
  4. Step 4: Simplify right side
    413x = 695,556
  5. Step 5: Solve for x
    x = 695,556/413
  6. Step 6: Final answer
    x = 1,684.15

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Why These Related Problems?

These problems maintain the same ratio (2.02) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.