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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 mL B. 1,900 mL C. 2,000 mL D. 2,100 mL E. 2,200 mL |
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| 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 mL B. 1,900 mL C. 2,000 mL D. 2,100 mL E. 2,200 mL Let W = the ORIGINAL volume of water in the mixture Let A = the ORIGINAL volume of acetone in the mixture A mixture contains nothing but water and acetone in a ratio of 1 : 2 We can write: W/A = 1/2 Cross multiply to get: 2W = A After 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 mixture And A = the volume of acetone in the NEW mixture So we can write: (W + 200)/A = 2/3 Cross multiply: 3(W + 200) = 2A Expand: 3W + 600 = 2A We now have the following system of equations: 2W = A 3W + 600 = 2A Take the top equation and multiply both sides by 2 to get: 4W = 2A 3W + 600 = 2A Since both equations are set equal to 2A, they must be equal: 4W = 3W + 600 Solve: W = 600 Since W = 600, and since we already know 2W = A, we can conclude that A = 1200 What is the original volume of the mixture ? Original volume = W + A = 600 + 1200 = 1800 Answer: A |
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| 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 mL B. 1,900 mL C. 2,000 mL D. 2,100 mL E. 2,200 mL Let the amount of water be x Acetone = 2x 200ml of water is added, which means no change in amount of acetone: \(\frac{x + 200}{2x }= \frac{2}{3}\) 3x + 600 = 4x x = 600 - Volume of water Volume of Acetone = 2x = 1200 Total volume = 1200 + 600 = 1800 - (A), IMO! |
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| 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 mL B. 1,900 mL C. 2,000 mL D. 2,100 mL E. 2,200 mL The volume of water and acetone in the original mixture can be written as: Water = 1x mL Acetone = 2x mL Since 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 = 1800mL Hence, answer is option A. |
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