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Finding the Third Proportional to 827.72 and 1,678.22

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Solution

The third proportional to 827.72 and 1,678.22 is: 3,402.63

Step by Step Solution

  1. Step 1: Write the proportion equation
    827.72 : 1,678.22 = 1,678.22 : x
  2. Step 2: Convert to fraction form
    827.72/1,678.22 = 1,678.22/x
  3. Step 3: Cross multiply
    827.72x = 1,678.22 × 1,678.22
  4. Step 4: Simplify right side
    827.72x = 2,816,418.17
  5. Step 5: Solve for x
    x = 2,816,418.17/827.72
  6. Step 6: Final answer
    x = 3,402.63

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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.