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Finding the Third Proportional to 405.84 and 824.34

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Solution

The third proportional to 405.84 and 824.34 is: 1,674.39

Step by Step Solution

  1. Step 1: Write the proportion equation
    405.84 : 824.34 = 824.34 : x
  2. Step 2: Convert to fraction form
    405.84/824.34 = 824.34/x
  3. Step 3: Cross multiply
    405.84x = 824.34 × 824.34
  4. Step 4: Simplify right side
    405.84x = 679,542.62
  5. Step 5: Solve for x
    x = 679,542.62/405.84
  6. Step 6: Final answer
    x = 1,674.39

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Why These Related Problems?

These problems maintain the same ratio (2.03) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.