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Finding the Third Proportional to 291.75 and 413.25

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Solution

The third proportional to 291.75 and 413.25 is: 585.35

Step by Step Solution

  1. Step 1: Write the proportion equation
    291.75 : 413.25 = 413.25 : x
  2. Step 2: Convert to fraction form
    291.75/413.25 = 413.25/x
  3. Step 3: Cross multiply
    291.75x = 413.25 × 413.25
  4. Step 4: Simplify right side
    291.75x = 170,775.56
  5. Step 5: Solve for x
    x = 170,775.56/291.75
  6. Step 6: Final answer
    x = 585.35

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Why These Related Problems?

These problems maintain the same ratio (1.42) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.