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Finding the Third Proportional to 9,824 and 11,072

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Solution

The third proportional to 9,824 and 11,072 is: 12,478.54

Step by Step Solution

  1. Step 1: Write the proportion equation
    9,824 : 11,072 = 11,072 : x
  2. Step 2: Convert to fraction form
    9,824/11,072 = 11,072/x
  3. Step 3: Cross multiply
    9,824x = 11,072 × 11,072
  4. Step 4: Simplify right side
    9,824x = 122,589,184
  5. Step 5: Solve for x
    x = 122,589,184/9,824
  6. Step 6: Final answer
    x = 12,478.54

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Why These Related Problems?

These problems maintain the same ratio (1.13) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.