By receiving two successive discounts, a dealer bought merchandise for $9 that was listed at $20. What were the discounts in percent if the first discount was 5 times the second?

• 50% and 10%
  
  Let the discounts be 5x and x ( given the first discount was 5 times the 2nd)
  
  1st discount = 20*5x/100 = x
  price after discount = (20-x)
  
  2nd discount = (20-x)*x/100
  price after discount = (20-x) - [(20-x)*x/100]
  given price after discount = 9
  so,
  (20-x) - [(20-x)*x/100] = 9
  100*(20-x) - (20-x)*x =900
  2000 - 100x -20x +x^2 = 900
  x^2 - 120x + 1100 = 0
  x^2 - 10x -110x + 1100 = 0
  x(x-10) -110(x-10) = 0
  (x-10)(x-110) = 0
  ===> x = 10 or 110
  so discounts are 5*10=50% and 10%
  
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