plz answer this mixture problem

[jagdeep]

i always get confused in this
q: solution is 90% glycerin . I f there are 4 gallons of solution then how much water in gallons must be added to make a 75% glycerin solution

a)1.8 b)1.4 c)1.2 d) 1.o e) 0.8

[nikilnikil]

4*10% + x*100%
______________ = 25%
4+x


cross multiply,
.4 + x = 1 + .25x

.75x = .6
x = .6/.75

so, x = .8


Method is simple. First , use only percentage of water or percentage of solution throughout the solution.

problem states: solution is 90% glycerin . I f there are 4 gallons of solution then how much water in gallons must be added to make a 75% glycerin solution

so, solution of 4 gallons contain 10% water and 90% glycerin. Since, we want to add additional water , let the entire equation be based on water.

so, (10%*4 + 100%* x) / (4+x) = 25% solution of water [ because we want a solution containing 75 % glycerine and 25%water.

Weighted average. So, divide the solution in numerator with total solution ( 4+x)

Cross multiply, you will get the answer.

Regards,
Nik

[jagdeep]

thanks a lot nik, it was so simple
thanks gain for telling me exact way to solve this

4*10% + x*100%
______________ = 25%
4+x


cross multiply,
.4 + x = 1 + .25x

.75x = .6
x = .6/.75

so, x = .8


Method is simple. First , use only percentage of water or percentage of solution throughout the solution.

problem states: solution is 90% glycerin . I f there are 4 gallons of solution then how much water in gallons must be added to make a 75% glycerin solution

so, solution of 4 gallons contain 10% water and 90% glycerin. Since, we want to add additional water , let the entire equation be based on water.

so, (10%*4 + 100%* x) / (4+x) = 25% solution of water [ because we want a solution containing 75 % glycerine and 25%water.

Weighted average. So, divide the solution in numerator with total solution ( 4+x)

Cross multiply, you will get the answer.

Regards,
Nik

[Leon1984]

The easiest way it to work with solid numbers. 90% out of 4 gallons is 3.6 gallons of glicerin. Now, you want this amount to be 75% or 3/4 of something. This means, that 3.6 is 3 quarters, and one quarter is 1.2. So what we need is just add another quarter, or 1.2 galons. HOWEVER! this is to be added to glicerin only, and since we have water left, we add this 1.2 disregarding the water, i.e 3.6+1.2=4.8 and since we have a total of 4 gallons, we need to add only 0.8.

Check: what is 3/4 or 75% of 4.8 gallons? ans- 3.6

Hope this helps.

[palvarez]

i always get confused in this
q: solution is 90% glycerin . I f there are 4 gallons of solution then how much water in gallons must be added to make a 75% glycerin solution

a)1.8 b)1.4 c)1.2 d) 1.o e) 0.8

The tricky part: translating water as 0 percent glycerin. Once ya get it right, everything goes smooth.

0======= 90
===75=====

15: 75 = 1:5


5 parts = 4 gallons
1 part = 4/5 = 0.8 gallons

[aspirant1]

am not able to get this equation (10%*4 + 100%* x) / (4+x) = 25% .......specifically 100%*x

[MG368]

this is how i did this problem:

90% of 4 gallons =3.6

so, now 3.6/ 4+x * 100%= 75%

where x = amount of water added, the glycerine amount will remain the same.

so x= 0.8

[nikilnikil]

am not able to get this equation (10%*4 + 100%* x) / (4+x) = 25% .......specifically 100%*x


Hello Aspirant1,

This is similar to weighted average.

see in the numerator 10% of 4 gallons will give you the content of water in 4 gallons
and 100% of x gallons will contain total water which has to be mixed with the original solution.

When you divide it by (4+X) it is nothing but weighted average of the entire solution which is equivalent to 25% water solution.

Hope this clears your doubt.

~Nik

[ssuarezo]

Hi:

Another easy way: Rule of 3:

If we want 3.6 to be the 75%, how much is 25%
So, x=3.6*.25/.75 = 1.2, but 0.4 already there, so x=0.8

Silvia