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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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Can some one explain when to use traditional mixture solutions using grid and when to use simple proportionality equations?
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rg1
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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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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Bunuel
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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Bunuel
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

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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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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Bunuel
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

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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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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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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rxs0005
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

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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rxs0005
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

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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(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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rxs0005
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


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
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Lets say , weight of the drink mix = x
hence 5/9x = sugar
4/9x = dye
7.5% of a gallon is dye .
1 * 75 / 1000 = 5/9 * x
x= 135/1000

Lets say that p% of 1 gallon is dye .
1 * p/ 100 = 4/9 * x
1 * p / 100 = 4/9 * 135 / 1000
p= 6
A is the answer.
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rxs0005
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
There is a drink mix. When the mix is added to water, a gallon of drink is made. May I ask why we are not calculating the quantity of water added?
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Raome
rxs0005
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

There is a drink mix. When the mix is added to water, a gallon of drink is made. May I ask why we are not calculating the quantity of water added?

First of all, it doesn't matter because the question does not ask about the amount of water. It only asks for the percentage of dye in the final gallon.

Also, some solutions in the thread do calculate the volume of the mix, which indirectly gives the water volume as 1 gallon minus that. So the water amount is implied, but not required directly.
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