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Finding the Third Proportional to 820 and 1,097

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Solution

The third proportional to 820 and 1,097 is: 1,467.57

Step by Step Solution

  1. Step 1: Write the proportion equation
    820 : 1,097 = 1,097 : x
  2. Step 2: Convert to fraction form
    820/1,097 = 1,097/x
  3. Step 3: Cross multiply
    820x = 1,097 × 1,097
  4. Step 4: Simplify right side
    820x = 1,203,409
  5. Step 5: Solve for x
    x = 1,203,409/820
  6. Step 6: Final answer
    x = 1,467.57

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Why These Related Problems?

These problems maintain the same ratio (1.34) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.