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Finding the Third Proportional to 4,097 and 5,754

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Solution

The third proportional to 4,097 and 5,754 is: 8,081.16

Step by Step Solution

  1. Step 1: Write the proportion equation
    4,097 : 5,754 = 5,754 : x
  2. Step 2: Convert to fraction form
    4,097/5,754 = 5,754/x
  3. Step 3: Cross multiply
    4,097x = 5,754 × 5,754
  4. Step 4: Simplify right side
    4,097x = 33,108,516
  5. Step 5: Solve for x
    x = 33,108,516/4,097
  6. Step 6: Final answer
    x = 8,081.16

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Why These Related Problems?

These problems maintain the same ratio (1.40) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.