Four-ninths of a drink mix is dye and the rest is sugar. Whe : Problem Solving (PS)

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Four-ninths of a drink mix is dye and the rest is sugar. Whe

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Director

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Four-ninths of a drink mix is dye and the rest is sugar. Whe [#permalink]

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25 Dec 2010, 06:26

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68% (02:22) correct

32% (02:45) wrong

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Four-ninths of a drink mix is dye and the rest is sugar. When the mix is added to water a gallon of drink is made that is 7.5% sugar. What percentage of the gallon is dye?

(A) 6
(B) 6.5
(C) 7.5
(D) 8
(E) 24

Spoiler: OA

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Re: Mixture problem [#permalink]

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25 Dec 2010, 07:47

The proportion of Dye and sugar will remain constant.

Dye/Sugar = (4/9)/(5/9) = x/7.5
=> 4/5 = x/7.5 => x = 4*7.5/5 = 6.

Answer is A.

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Re: Mixture problem [#permalink]

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25 Dec 2010, 07:49

I use a very simple way with fractions to find the calue of x:

$\frac{4}{9}/\frac{x}{100} = \frac{5}{9}/\frac{7,5}{100}$

When you solve it you will find that x=6

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Re: Mixture problem [#permalink]

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25 Dec 2010, 08:41

Can some one explain when to use traditional mixture solutions using grid and when to use simple proportionality equations?
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Re: Mixture problem [#permalink]

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25 Dec 2010, 17:20

rg1 wrote:

Can some one explain when to use traditional mixture solutions using grid and when to use simple proportionality equations?

Here you are adding the whole mixture to water, also the ratio water to sugar remains unchanged.

Also you only have to make simple comptutation: 7,5/5*4=6
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Re: Four-ninths of a drink mix is dye and the rest is sugar. Whe [#permalink]

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16 Dec 2013, 05:42

rxs0005 wrote:

Here, let's say that the gallon is 100 litres.
Then sugar in the gallon will be 7.5 litres
Now 5/9x=7.5
'x' is the amoung of the mix poured into gallon
x = (9)(1.5)

Now dye will be 9(1.5)*(4/9)=1.5*4=6

Hence A

Even if you don't find the way to solve it you can straight eliminate answers C,D,E cause the amount of dye is always going to be less given the
4:5 ratio

Hope it helps
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Re: Four-ninths of a drink mix is dye and the rest is sugar. Whe [#permalink]

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14 Jan 2015, 20:57

In the drink mix, if $\frac{4}{9} =$ dye, then

sugar $= 1 - \frac{4}{9} = \frac{5}{9}$

If sugar constitutes $\frac{7.5}{100}$, then dye percentage $= \frac{7.5}{100} * \frac{4}{9} * \frac{9}{5} = \frac{6}{100} = 6%$

Answer = A
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Four-ninths of a drink mix is dye and the rest is sugar. When the mix [#permalink]

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28 Jan 2017, 12:49

Bunuel wrote:

Four-ninths of a drink mix is dye and the rest is sugar. When the mix is added to water a gallon of drink is made that is 7.5% sugar. What percentage of the gallon is dye?

A. 6
B. 6.5
C. 7.5
D. 8
E. 24

ratio of sugar in mix to sugar in gallon=(5/9)/.075
ratio of dye in mix to dye in gallon=(4/9)/x
(5/9)/(.075)=(4/9)/x
x=6/100=6%
A

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Re: Four-ninths of a drink mix is dye and the rest is sugar. When the mix [#permalink]

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29 Jan 2017, 02:38

Bunuel wrote:

suppose it is a litre instead of gallon (As 1 litre =1000 ml)

7.5 % of a litre of solution is sugar
75ml is sugar
Now 75 ml sugar constitutes 5/9 of initial mixture
means 55.55% of initial mixture
means initial mixture is 134 ml thus dye is ~45%(ie 4/9) of 134 ml
thus 60 ml
so 60ml is 6% of 1000ml ie 1Litre

Ans A

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Re: Four-ninths of a drink mix is dye and the rest is sugar. When the mix [#permalink]

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29 Jan 2017, 09:38

Is answer A ? Let x be volume of dye. sugar is 5/9x.
5/9x = 7.5/100.

x= 27/200.
dye % = 4/9 * 27/200 *100 = 6%

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Re: Four-ninths of a drink mix is dye and the rest is sugar. When the mix [#permalink]

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29 Jan 2017, 11:47

Bunuel wrote:

A is the answer.

4/9 is dye , 5/9 sugar

5/9 represent 7.5 %
4/9 represent X

(4/9*7.5)/5/9
6 we will get....

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Re: Four-ninths of a drink mix is dye and the rest is sugar. When the mix [#permalink]

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07 May 2017, 14:40

Let initial amount be 9.
so dye equals 4 parts and sugar equals 5 parts.

now, 5 parts is 7.5% of the total. let total amount now be = a.
thus 7.5/100 a = 5.
a = 500/7.5

we need sugar / total
sugar hasn't changed so : 4/a = 4/ (500/7.5) = 0.06.
thus 6%

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Four-ninths of a drink mix is dye and the rest is sugar. Whe [#permalink]

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29 Oct 2017, 12:02

Say, Dye = 4, Sugar=5
We can find the equation below:
5= (9+water) *.075
Water= 57.66
Now,percentage of dye is:-
5/(57.66+9)
= .06
Or 6%

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Re: Four-ninths of a drink mix is dye and the rest is sugar. Whe [#permalink]

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31 Oct 2017, 16:42

rxs0005 wrote:

Since 4/9 of the drink mix is dye, 5/9 of the mix is sugar. We can create the following proportion in which n = the percentage of dye:

(4/9)/(5/9) = n/(7.5/100)

4/5 = 100n/7.5

500n = 30

n = 30/500 = 6/100 = 6%

Answer: A
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Re: Four-ninths of a drink mix is dye and the rest is sugar. Whe [#permalink]

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21 Nov 2017, 05:07

rxs0005 wrote:

Responding to a pm:

Quote:

is it possible to apply scale method to this one..?

You have 3 elements here - dye, sugar and water. So we cannot use the scale method.

We see that sugar is 5/9 of the drink and 7.5% of the entire water solution.
Dye which is 4/9 of the drink would be (7.5/5)*4 = 6% of the entire water solution

Answer (A)
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Re: Four-ninths of a drink mix is dye and the rest is sugar. Whe [#permalink]

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21 Nov 2017, 05:19

(4/9)/(5/9) = x/7.5
=> 4/5 = x/7.5 => x = 4*7.5/5 = 6.

So answer should be A
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Re: Four-ninths of a drink mix is dye and the rest is sugar. Whe [#permalink]

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26 Feb 2018, 03:34

rxs0005 wrote:

Let X be the total vol of mix
Dye = 4/9*X
Sugar = 5/9*X

[color=#ffff00]Volume of sugar and dye remain unchanged

Therefore conc of Sugar in final mix = total sugar/1 gallon = 7.5% ( Given)[/color]

= (5/9*x)/1 = 7.5
=5X= 67.5 ===> x = 13.5

Hence dye percentage = 4/9*13.5 = 6

Answer A 6