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Finding the Third Proportional to 2,065 and 3,097

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Solution

The third proportional to 2,065 and 3,097 is: 4,644.75

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,065 : 3,097 = 3,097 : x
  2. Step 2: Convert to fraction form
    2,065/3,097 = 3,097/x
  3. Step 3: Cross multiply
    2,065x = 3,097 × 3,097
  4. Step 4: Simplify right side
    2,065x = 9,591,409
  5. Step 5: Solve for x
    x = 9,591,409/2,065
  6. Step 6: Final answer
    x = 4,644.75

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.