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Finding the Third Proportional to 823.50 and 1,809

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Solution

The third proportional to 823.50 and 1,809 is: 3,973.87

Step by Step Solution

  1. Step 1: Write the proportion equation
    823.50 : 1,809 = 1,809 : x
  2. Step 2: Convert to fraction form
    823.50/1,809 = 1,809/x
  3. Step 3: Cross multiply
    823.50x = 1,809 × 1,809
  4. Step 4: Simplify right side
    823.50x = 3,272,481
  5. Step 5: Solve for x
    x = 3,272,481/823.50
  6. Step 6: Final answer
    x = 3,973.87

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Why These Related Problems?

These problems maintain the same ratio (2.20) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.