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Finding the Third Proportional to 829.97 and 1,205.86

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Solution

The third proportional to 829.97 and 1,205.86 is: 1,751.99

Step by Step Solution

  1. Step 1: Write the proportion equation
    829.97 : 1,205.86 = 1,205.86 : x
  2. Step 2: Convert to fraction form
    829.97/1,205.86 = 1,205.86/x
  3. Step 3: Cross multiply
    829.97x = 1,205.86 × 1,205.86
  4. Step 4: Simplify right side
    829.97x = 1,454,096.83
  5. Step 5: Solve for x
    x = 1,454,096.83/829.97
  6. Step 6: Final answer
    x = 1,751.99

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Why These Related Problems?

These problems maintain the same ratio (1.45) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.