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Finding the Third Proportional to 259.50 and 413.63

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Solution

The third proportional to 259.50 and 413.63 is: 659.29

Step by Step Solution

  1. Step 1: Write the proportion equation
    259.50 : 413.63 = 413.63 : x
  2. Step 2: Convert to fraction form
    259.50/413.63 = 413.63/x
  3. Step 3: Cross multiply
    259.50x = 413.63 × 413.63
  4. Step 4: Simplify right side
    259.50x = 171,085.64
  5. Step 5: Solve for x
    x = 171,085.64/259.50
  6. Step 6: Final answer
    x = 659.29

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Why These Related Problems?

These problems maintain the same ratio (1.59) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.