Problem Solving

5. A mixture of 12 ounces of vinegar and oil is 40%n vinegar by weight. How many ounces of oil must be added to the mixtue to produce a new mixture that is only 25% vinegar?

answer?


I dont know the answer but I Came up with 20?
Pls help

12 onces mixture of 40% vinegar is 4.8 ounces vinegar and 7.2 oil.

For a solution to be 25% vinegar, the 4.8 ounces must constitute 1/4th of the solution.
Or the solution should contain 19.2 ounces. (4.8/19.2 = 1/4)

Since we already have 12 ounces of solution, we need to add (19.2-12) 7.2 ounces of oil

we need to obtain the proportion of V/(V+O)=0.25 from the proportion of (0.4*12)/(0.4*12 + 0.6*12) where "V" is vinegar and "O" is oil; the present volume of vinegar is (0.4*12) ounces

the volume of vinegar stays the same, as we add only oil ==> (0.4*12)/(0.4*12+O)=0.25
by solving this equation we get 4.8/(4.8+O)=0.25 OR 4.8/0.25=4.8+O <> 19.2-4.8=O and O=14.4

the initial volume of "O" was 12*0.6 and we need to subtract this from 14.4, hence 14.4-7.2=7.2 ounces

the short-cut is when we simply click 4.8/(12+Oil)=0.25 where Oil is additional oil required

cmal wrote:5. A mixture of 12 ounces of vinegar and oil is 40%n vinegar by weight. How many ounces of oil must be added to the mixtue to produce a new mixture that is only 25% vinegar?

answer?


I dont know the answer but I Came up with 20?
Pls help

cmal wrote:5. A mixture of 12 ounces of vinegar and oil is 40%n vinegar by weight. How many ounces of oil must be added to the mixtue to produce a new mixture that is only 25% vinegar?

answer?


I dont know the answer but I Came up with 20?
Pls help

Another approach:

40% of the original mixture is vinegar and 60% is oil:
Vinegar : Oil = 4:6 = 2:3.

If the amount of OIL doubles:
Vinegar : Oil = 2:6 = 1:3.
The ratio above indicates that, of every 4 ounces, 1 ounce will be vinegar and 3 ounces will be oil, yielding a mixture that is 1/4 vinegar.

Thus, the amount of oil must double.
Since the amount of oil in the original mixture = .6(12) = 7.2 ounces, another 7.2 ounces of oil must be added.

we know that an initial mixture consists of 7.2 ounces of oil (12* (100%-40%)=7.2)
we also know, that a new mixture has 75% (or 3/4)oil (100%-25%)

now we have
(7.2+x)/(12+x)=3/4

x=7.2

I had a main problem in understanding this question, I don't but maybe because I'm not a native english speaker,my mistake was that I didn't get how we multiplied (0.40)(12) in the first place, the question says that
A mixture of 12 ounces of vinegar and oil is 40 percent vinegar, I understood from this that
12 = 0.40Vinegar
not 12 of Vinegar which means 12 * 0.40

because for me there is a difference in translating the verbal information in the question stem

is means =
of means "multiplication"

but in this question you used the multiplication and this is what I missed from the beginning.

I tried to solve this problem by using the alligation method.

40% vinegar ----------- 25% vinegar ------------ 0% vinegar
=> vinegar : oil = 25 : 15 or 5 : 3

I don't know what to do next...

talaangoshtari wrote:I tried to solve this problem by using the alligation method.

40% vinegar ----------- 25% vinegar ------------ 0% vinegar
=> vinegar : oil = 25 : 15 or 5 : 3

I don't know what to do next...

The portion in red misstates the ratio.
The resulting ratio is between the ORIGINAL SOLUTION and the added PURE OIL:
(original solution) : (added pure oil) = 5:3.

Implication:
For every 5 parts original solution, there must be 3 parts added pure oil.
In other words, the 12 ounces of original solution must constitute 5/8 of the resulting volume:
12 = (5/8)x
x = 96/5.

Thus:
Amount of added pure oil = (total resulting volume) - (volume of original solution) = 96/5 - 12 = 96/5 - 60/5 = 36/5 = 7.2 ounces.

I think Simplest way to solve

Vinegar amount remain same in both solutions. x is amount of oil needed

40/100 * 12 = 25/100 (12+x)
and solve for x
4.8 =1/4(12+x)
4.8 *4 = 12 + x
19.2-12 = x
x=7.2