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Finding the Third Proportional to 823.22 and 1,782.84

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Solution

The third proportional to 823.22 and 1,782.84 is: 3,861.10

Step by Step Solution

  1. Step 1: Write the proportion equation
    823.22 : 1,782.84 = 1,782.84 : x
  2. Step 2: Convert to fraction form
    823.22/1,782.84 = 1,782.84/x
  3. Step 3: Cross multiply
    823.22x = 1,782.84 × 1,782.84
  4. Step 4: Simplify right side
    823.22x = 3,178,531.84
  5. Step 5: Solve for x
    x = 3,178,531.84/823.22
  6. Step 6: Final answer
    x = 3,861.10

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Why These Related Problems?

These problems maintain the same ratio (2.17) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.