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# Jim needs to mix a solution in the following ratio: 1 part

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Jim needs to mix a solution in the following ratio: 1 part [#permalink]  06 Nov 2012, 12:46
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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:
$$\frac{x}{2} + 4x = 18$$ $$=> x=4$$
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.
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Last edited by Bunuel on 07 Nov 2012, 01:54, edited 1 time in total.
Renamed the topic.
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Re: Confusing Ratios question [#permalink]  06 Nov 2012, 19:29
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, 22:50
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, 19:46
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
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Re: Jim needs to mix a solution in the following ratio: 1 part [#permalink]  06 Jun 2013, 14:30
as vy3rgc mentioned, 1/2:4 ratio is a 1:8 ratio.

I figured it out this way.
in a 10 part solution, there is 2 bleach and 8 water.
Jim only added 1/2 the amount of bleach needed so instead of 2 bleach he added 1 bleach and 8 water.
This also changes it from a 10 part mixed solution to a 9 part mixed solution.

In a 18 part solution with this mistake, he'll have 2 parts bleach and 16 parts water.
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Re: Jim needs to mix a solution in the following ratio: 1 part [#permalink]  07 Apr 2015, 22:32
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Re: Jim needs to mix a solution in the following ratio: 1 part [#permalink]  08 Apr 2015, 22:29
Expert's post
Hi All,

While this is an old series of posts, there is a rather straight-forward way to approach this question that is more about real-world math than anything else.

The original prompt tells us that Jim needs to mix a solution in the following ratio: 1 part bleach for every 4 parts water.

So, if we have 1 part bleach + 4 parts water we get 5 parts total mixture....

Next, we're told that when mixing the solution, Jim makes a mistake and mixes in half as much bleach as he ought to have.

So, he ACTUALLY mixed 1/2 part bleach + 4 parts water and gets 4.5 parts total mixture....

The total solution consists of 18 mL. How much did Jim put into the solution?

18 = (4.5)(4) so the 18mL is made up of 4 "sets" of the 4.5 parts mixture. This means there are 4(4) = 16 mL of water and 4(1/2) = 2mL of bleach.

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Re: Jim needs to mix a solution in the following ratio: 1 part   [#permalink] 08 Apr 2015, 22:29
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