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Finding the Third Proportional to 822.75 and 1,209.75

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Solution

The third proportional to 822.75 and 1,209.75 is: 1,778.78

Step by Step Solution

  1. Step 1: Write the proportion equation
    822.75 : 1,209.75 = 1,209.75 : x
  2. Step 2: Convert to fraction form
    822.75/1,209.75 = 1,209.75/x
  3. Step 3: Cross multiply
    822.75x = 1,209.75 × 1,209.75
  4. Step 4: Simplify right side
    822.75x = 1,463,495.06
  5. Step 5: Solve for x
    x = 1,463,495.06/822.75
  6. Step 6: Final answer
    x = 1,778.78

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Why These Related Problems?

These problems maintain the same ratio (1.47) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.