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Finding the Third Proportional to 824.25 and 1,782.75

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Solution

The third proportional to 824.25 and 1,782.75 is: 3,855.87

Step by Step Solution

  1. Step 1: Write the proportion equation
    824.25 : 1,782.75 = 1,782.75 : x
  2. Step 2: Convert to fraction form
    824.25/1,782.75 = 1,782.75/x
  3. Step 3: Cross multiply
    824.25x = 1,782.75 × 1,782.75
  4. Step 4: Simplify right side
    824.25x = 3,178,197.56
  5. Step 5: Solve for x
    x = 3,178,197.56/824.25
  6. Step 6: Final answer
    x = 3,855.87

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Why These Related Problems?

These problems maintain the same ratio (2.16) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.