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 Author: Bunuel [ 08 Jul 2021, 05:30 ] Post subject: A mixture contains nothing but water and acetone in a ratio of 1 : 2. A mixture contains nothing but water and acetone in a ratio of 1 : 2. After 200 mL of water is added to the mixture, the ratio of water to acetone is 2 : 3. What is the original volume of the mixture ? A. 1,800 mLB. 1,900 mLC. 2,000 mLD. 2,100 mLE. 2,200 mL

 Author: BrentGMATPrepNow [ 08 Jul 2021, 05:39 ] Post subject: A mixture contains nothing but water and acetone in a ratio of 1 : 2. Bunuel wrote:A mixture contains nothing but water and acetone in a ratio of 1 : 2. After 200 mL of water is added to the mixture, the ratio of water to acetone is 2 : 3. What is the original volume of the mixture ? A. 1,800 mLB. 1,900 mLC. 2,000 mLD. 2,100 mLE. 2,200 mLLet W = the ORIGINAL volume of water in the mixtureLet A = the ORIGINAL volume of acetone in the mixtureA mixture contains nothing but water and acetone in a ratio of 1 : 2We can write: W/A = 1/2Cross multiply to get: 2W = AAfter 200 mL of water is added to the mixture, the ratio of water to acetone is 2 : 3.So, W + 200 = the volume of water in the NEW mixtureAnd A = the volume of acetone in the NEW mixtureSo we can write: (W + 200)/A = 2/3Cross multiply: 3(W + 200) = 2AExpand: 3W + 600 = 2AWe now have the following system of equations: 2W = A3W + 600 = 2ATake the top equation and multiply both sides by 2 to get:4W = 2A3W + 600 = 2A Since both equations are set equal to 2A, they must be equal: 4W = 3W + 600Solve: W = 600Since W = 600, and since we already know 2W = A, we can conclude that A = 1200What is the original volume of the mixture ? Original volume = W + A = 600 + 1200 = 1800 Answer: A

 Author: Showmeyaa [ 08 Jul 2021, 12:37 ] Post subject: Re: A mixture contains nothing but water and acetone in a ratio of 1 : 2. Bunuel wrote:A mixture contains nothing but water and acetone in a ratio of 1 : 2. After 200 mL of water is added to the mixture, the ratio of water to acetone is 2 : 3. What is the original volume of the mixture ? A. 1,800 mLB. 1,900 mLC. 2,000 mLD. 2,100 mLE. 2,200 mLLet the amount of water be xAcetone = 2x200ml of water is added, which means no change in amount of acetone:$$\frac{x + 200}{2x }= \frac{2}{3}$$3x + 600 = 4xx = 600 - Volume of waterVolume of Acetone = 2x = 1200Total volume = 1200 + 600 = 1800 - (A), IMO!

 Author: tanyas311 [ 28 Sep 2022, 04:41 ] Post subject: A mixture contains nothing but water and acetone in a ratio of 1 : 2. Bunuel wrote:A mixture contains nothing but water and acetone in a ratio of 1 : 2. After 200 mL of water is added to the mixture, the ratio of water to acetone is 2 : 3. What is the original volume of the mixture ? A. 1,800 mLB. 1,900 mLC. 2,000 mLD. 2,100 mLE. 2,200 mLThe volume of water and acetone in the original mixture can be written as:Water = 1x mLAcetone = 2x mLSince 200mL water is added to the mixture giving the new ratio as 2:3$$(1x+200)/2x=2/3$$$$3x+600=4x$$$$x=600$$Original Mixture = 3x = 3*600 = 1800mLHence, answer is option A.

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