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Finding the Third Proportional to 413.75 and 563.50

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Solution

The third proportional to 413.75 and 563.50 is: 767.45

Step by Step Solution

  1. Step 1: Write the proportion equation
    413.75 : 563.50 = 563.50 : x
  2. Step 2: Convert to fraction form
    413.75/563.50 = 563.50/x
  3. Step 3: Cross multiply
    413.75x = 563.50 × 563.50
  4. Step 4: Simplify right side
    413.75x = 317,532.25
  5. Step 5: Solve for x
    x = 317,532.25/413.75
  6. Step 6: Final answer
    x = 767.45

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Why These Related Problems?

These problems maintain the same ratio (1.36) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.