A cask contains 12 gallons of mixture of wine and water in the ratio 3:1. how much of the mixture must be drawn off and water substituted so the wine and water become half and half.

• in 12 gallons mixture wine=12*3/4=9 gallons and water=3 gallons
  if we draw 4 gallons of mixture..
  so in 4 gallons wine=3 gallons and water=1 gallons...
  remaining mixture wine=6 gallons and water =2 gallons
  then we mix 4 gallon water to the mixture..
  after adding water wine =6 gallon and water =6 gallon..
  so wine:water=6:6=1:1
  so we have to draw 4 gallons mixture....
• 9 years agoHelpfull: Yes(16) No(4)
• let the mixture is x
  in 12 gallons,wine is 12*(3/4)=9 gallons,and water is 3 gallons
  now in x gallons,wine will be x*(3/4) and water will be (x/4).
  according to question their ratio will be 1:1 in the new mixture...
  so equation becomes
  9-(3*x)/4=3-(x/4)+x
  and the answer is x=4
  
• 9 years agoHelpfull: Yes(15) No(1)
• given,
  12 gallons of mixture so that in 3:1 ratio
  (wine=12*3/4=9 gallons & water=3 gallons)
  we draw x gallons from mixture,
  now,for ratio of wine & water to be 1:1
  so, 9:(3+x)=1:1
  => x=6
  Hence, 6gallons of the mixture must be drwan off and water substituted so the wine and water become half and half.
  
• 9 years agoHelpfull: Yes(0) No(16)
• wine=12*(3/4)=9 gallons and water = 3 gallons
  9/(3+x)=1
  x=6
  
• 8 years agoHelpfull: Yes(0) No(5)
• ANS: 6 GALLONS
  3*3 of wine and 3*1 of water
  become 1:1 we add 3*2 of water
• 8 years agoHelpfull: Yes(0) No(1)
• 12*3/4=9 gallons wine& 12*1/4=3gallons water in 12 gallons mixture
  now let x gallons be drawn off
  so,
  (9 - 3x/4) / (3 - x/4 + x) = 1
  => x=4 gallons
• 8 years agoHelpfull: Yes(0) No(0)
• 1/2(12)=3-x/4+x
  x=4
• 7 years agoHelpfull: Yes(0) No(0)