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# A 7.5 liter mixture of water and sugar is 60% sugar. If 1.5

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Manager
Joined: 04 Jan 2013
Posts: 75
A 7.5 liter mixture of water and sugar is 60% sugar. If 1.5  [#permalink]

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Updated on: 09 Jan 2013, 03:19
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5% (low)

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91% (00:56) correct 9% (02:00) wrong based on 159 sessions

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A 7.5 liter mixture of water and sugar is 60% sugar. If 1.5 liters of water is added, approximately what is the % of the new mixture of sugar?

A. 40%
B. 50%
C. 63%
D. 64%
E. 68

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Originally posted by chiccufrazer1 on 08 Jan 2013, 13:08.
Last edited by Bunuel on 09 Jan 2013, 03:19, edited 1 time in total.
Renamed the topic and edited the question.
Manager
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Re: A 7.5 litre mixture of water and sugar is 60%sugar.if 1.5 li  [#permalink]

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08 Jan 2013, 13:23
multiply 7.5 by 10...so 75 Liters of solution which is 30 L Water and 45L Sugar

If you add 1.5x10 (15 L) of water the overall solution will contain 90L. Of that 90L 45L is water and 45 L is sugar.

Manager
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Re: A 7.5 litre mixture of water and sugar is 60%sugar.if 1.5 li  [#permalink]

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08 Jan 2013, 13:32
Ya sambam ofcos the official answer is B.50 percent but am not satisified with how i got it..this is how i did it.if 7.5 =60% therefore 1.5 would equal 12.i decided to represent 1.5 as 1 part of water and hence in 7.5 i had 5 parts of water..the addition of water will made the new mixture to have 6 parts of water and a less percentage of sugar when i added 1.5 litres.. I said to myself that if 5 parts of water represent 60percent sugar then 6 parts will have to represent a small percentage of sugar i.e (5*60/6)%..thanks for making it clear to me!:-)

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Re: A 7.5 liter mixture of water and sugar is 60% sugar. If 1.5  [#permalink]

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29 Dec 2017, 13:49
Top Contributor
chiccufrazer1 wrote:
A 7.5 liter mixture of water and sugar is 60% sugar. If 1.5 liters of water is added, approximately what is the % of the new mixture of sugar?

A. 40%
B. 50%
C. 63%
D. 64%
E. 68

ASIDE: We can eliminate C, D and E immediately (without performing any calculations).
Here's why: If we begin with a mixture that's 60% sugar and then we dilute it by adding water, the resulting mixture will have less than 60% sugar. So, eliminate C, D and E.

Okay, on to the solution.

7.5 liter mixture of water and sugar is 60% sugar.
60% of 7.5 liters is sugar
60% of 7.5 = 4.5, so the 4.5 mixture has 4.5 liters of sugar

1.5 liters of water is added
So, the volume of the new mixture is 9 liters.
Since no sugar was added, the volume of the sugar is still 4.5 liters

(4.5)/9 = 1/2 = 50%
So, the new mixture is [spoiler]50% sugar[/spoiler].

Cheers,
Brent
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A 7.5 liter mixture of water and sugar is 60% sugar. If 1.5  [#permalink]

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29 Dec 2017, 16:31
chiccufrazer1 wrote:
A 7.5 liter mixture of water and sugar is 60% sugar. If 1.5 liters of water is added, approximately what is the % of the new mixture of sugar?

A. 40%
B. 50%
C. 63%
D. 64%
E. 68
If you are used to weighted averages. . .

Water has 0.0 percent sugar, but it is being added

$$.6(7.5) + 0.0(1.5) = \frac{x}{100}(7.5 + 1.5)$$
Both sides * 100:
$$6(75) = 9x$$
$$450 = 9x$$
$$x = 50$$ percent

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Re: A 7.5 liter mixture of water and sugar is 60% sugar. If 1.5  [#permalink]

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31 Dec 2017, 11:31
chiccufrazer1 wrote:
A 7.5 liter mixture of water and sugar is 60% sugar. If 1.5 liters of water is added, approximately what is the % of the new mixture of sugar?

A. 40%
B. 50%
C. 63%
D. 64%
E. 68

Posted from my mobile device

Initial ratio of Water and Sugar $$= 40: 60 = 2: 3$$

Thus, the amount of water $$= \frac{2}{(2+3)} * 7.5 = 3$$ liters and the amount of sugar $$= \frac{3}{(2+3)} * 7.5 = 4.5$$ liters

Water added $$= 1.5$$ liters

Thus, total amount of water and sugar mixture $$= 7.5 + 1.5 = 9$$ liters

Percentage of sugar $$= \frac{4.5}{9} = 50$$ liters

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Saquib
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Re: A 7.5 liter mixture of water and sugar is 60% sugar. If 1.5 &nbs [#permalink] 31 Dec 2017, 11:31
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