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Jim needs to mix a solution in the following ratio: 1 part [#permalink]
 06 Nov 2012, 13:46
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I can not seem grasp the reasoning behind the Answer to the below question: Jim needs to mix a solution in the following ratio: 1 part bleach for every 4 parts water. When mixing the solution, Jim makes a mistake and mixes in half as much bleach as he ought to have. The total solution consists of 18 mL. How much did Jim put into the solution?To solve this problem: The ratio is 1:4, meaning there should be x parts bleach and 4x parts water. However, Jim put in half as much bleach as he should have, so he put in \frac{x}{2} parts bleach. So the equation would be: \frac{x}{2} + 4x = 18 => x=4This part is clear, however, according to the MGMAT Guide the correct answer is not 4, but it's \frac{4}{2}, but we already used \frac{x}{2} in the equation. Now, 4(2) + 2 = 18 which makes sense. However, my main concern is with the reasoning, that to solve the equation, we have already halved Jim's amount, and then we are halving it again. Please explain.
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Last edited by Bunuel on 07 Nov 2012, 02:54, edited 1 time in total.
Renamed the topic.
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Re: Confusing Ratios question [#permalink]
06 Nov 2012, 20:29
megafan wrote: I can not seem grasp the reasoning behind the Answer to the below question:
Jim needs to mix a solution in the following ratio: 1 part bleach for every 4 parts water. When mixing the solution, Jim makes a mistake and mixes in half as much bleach as he ought to have. The total solution consists of 18 mL. How much did Jim put into the solution?
To solve this problem:
The ratio is 1:4, meaning there should be x parts bleach and 4x parts water. However, Jim put in half as much bleach as he should have, so he put in \frac{x}{2} parts bleach. So the equation would be:
\frac{x}{2} + 4x = 18 => x=4
This part is clear, however, according to the MGMAT Guide the correct answer is not 4, but it's \frac{4}{2}, but we already used \frac{x}{2} in the equation.
Now, 4(2) + 2 = 18 which makes sense. However, my main concern is with the reasoning, that to solve the equation, we have already halved Jim's amount, and then we are halving it again. Please explain. if you look at the equation that you've set up. you would notice that you actually added x/2 part of bleach in 4x water not x part. Thus if x=4, the amount of bleach is x/2=4/2. It is not x that you are looking for, but the value that you used in mixture ie x/2
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Re: Confusing Ratios question [#permalink]
26 Nov 2012, 23:50
Vips0000 wrote: megafan wrote: I can not seem grasp the reasoning behind the Answer to the below question:
Jim needs to mix a solution in the following ratio: 1 part bleach for every 4 parts water. When mixing the solution, Jim makes a mistake and mixes in half as much bleach as he ought to have. The total solution consists of 18 mL. How much did Jim put into the solution?
To solve this problem:
The ratio is 1:4, meaning there should be x parts bleach and 4x parts water. However, Jim put in half as much bleach as he should have, so he put in \frac{x}{2} parts bleach. So the equation would be:
\frac{x}{2} + 4x = 18 => x=4
This part is clear, however, according to the MGMAT Guide the correct answer is not 4, but it's \frac{4}{2}, but we already used \frac{x}{2} in the equation.
Now, 4(2) + 2 = 18 which makes sense. However, my main concern is with the reasoning, that to solve the equation, we have already halved Jim's amount, and then we are halving it again. Please explain. if you look at the equation that you've set up. you would notice that you actually added x/2 part of bleach in 4x water not x part. Thus if x=4, the amount of bleach is x/2=4/2. It is not x that you are looking for, but the value that you used in mixture ie x/2 I dont understand what you are aiming to do here.. can you please clarify your explanation??
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Re: Jim needs to mix a solution in the following ratio: 1 part [#permalink]
24 May 2013, 20:46
megafan wrote: I can not seem grasp the reasoning behind the Answer to the below question:
Jim needs to mix a solution in the following ratio: 1 part bleach for every 4 parts water. When mixing the solution, Jim makes a mistake and mixes in half as much bleach as he ought to have. The total solution consists of 18 mL. How much did Jim put into the solution?
To solve this problem:
The ratio is 1:4, meaning there should be x parts bleach and 4x parts water. However, Jim put in half as much bleach as he should have, so he put in \frac{x}{2} parts bleach. So the equation would be:
\frac{x}{2} + 4x = 18 => x=4
This part is clear, however, according to the MGMAT Guide the correct answer is not 4, but it's \frac{4}{2}, but we already used \frac{x}{2} in the equation.
Now, 4(2) + 2 = 18 which makes sense. However, my main concern is with the reasoning, that to solve the equation, we have already halved Jim's amount, and then we are halving it again. Please explain. 1 part bleach for every 4 parts water = 1:4 1/2 part bleach for every 4 parts water = 1/2 : 4 = 1:8 9x = 18 x = 2 <-- Answer
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Re: Jim needs to mix a solution in the following ratio: 1 part
[#permalink]
24 May 2013, 20:46
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