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Finding the Third Proportional to 413.75 and 546.38

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Solution

The third proportional to 413.75 and 546.38 is: 721.51

Step by Step Solution

  1. Step 1: Write the proportion equation
    413.75 : 546.38 = 546.38 : x
  2. Step 2: Convert to fraction form
    413.75/546.38 = 546.38/x
  3. Step 3: Cross multiply
    413.75x = 546.38 × 546.38
  4. Step 4: Simplify right side
    413.75x = 298,525.64
  5. Step 5: Solve for x
    x = 298,525.64/413.75
  6. Step 6: Final answer
    x = 721.51

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Why These Related Problems?

These problems maintain the same ratio (1.32) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.