A solution is made up of 13 parts water, 2 parts orange juice, and 4

Question

A solution is made up of 13 parts water, 2 parts orange juice, and 4 parts apple juice. If you wanted the percentage of orange juice to be 25% of the solution, how many parts would you need to add?

A. 1/4
B. 3/11
C. 2
D. 3
E. 11/3

EvenPrime · Answer

Here is my attempt:

Current split up: W:O:A == 13:2:4

Current ratio of orange juice = 2/19

We want to know how many parts of orange juice to be added, to convert 2/19 to 1/4 (25%)

Problem formulation: 
((2+x) / (13 + 2+ x+ 4)) = 1/4, assuming x is the parts of orange juice to be added (x will be the answer)

(As we add parts of orange in numerator, the total in the denominator should also add up correspondingly)

On solving,

(2 + x) / (19 + x) = 1/4
8 + 4x = 19 + x
3x = 11
x = 11/3

Answer (E)

Archit3110 · Answer

given
w=13
o=2
a=4
total = 19
o ratio 2/19
we want o to be 25% 
13+x/19+x= 1/4
solve for x ; 11/3
IMO E

gracie · Answer

let p=parts of orange juice to be added
2+p=(19+p)/4→
p=11/3
E

ScottTargetTestPrep · Answer

Let N = the amount of orange juice that needs to be added. We can create the equation:

(2 + N)/(13 + 2 + 4 + N) = 1/4

4(2 + N) = 13 + 2 + 4 + N

8 + 4N = 19 + N

3N = 11

N = 11/3

Answer: E

LeoN88 · Answer

Given Solution= 13 + 2 +4

Now to reach the answer let's add x parts of orange.

New solution total= 13 + 2 + 4 + x
Orange Juice total= 2+x
So,

(2+x)/(13 + 2 + 4 + x) = 1/4

x=11/3

kanthaliya · Answer

Bunuel

I tried to solve in a different way, but I am not getting answer. Please tell me where I amota going wrong:

let the initial solution be x
Orange juice = (2/19)x
Orange juice added=y
therefore orange juice = (2/19)x + y and this is equal to 25%(x+y)
y=(11/57)x

Please help me I am totally confused

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A solution is made up of 13 parts water, 2 parts orange juice, and 4

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