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Finding the Third Proportional to 824 and 2,243

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Solution

The third proportional to 824 and 2,243 is: 6,105.64

Step by Step Solution

  1. Step 1: Write the proportion equation
    824 : 2,243 = 2,243 : x
  2. Step 2: Convert to fraction form
    824/2,243 = 2,243/x
  3. Step 3: Cross multiply
    824x = 2,243 × 2,243
  4. Step 4: Simplify right side
    824x = 5,031,049
  5. Step 5: Solve for x
    x = 5,031,049/824
  6. Step 6: Final answer
    x = 6,105.64

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Why These Related Problems?

These problems maintain the same ratio (2.72) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.