How many liters of an 8% solution of salt should be added to a 24% solution in order to obtain 928 liters of an 12% solution?

Question

I can't figure this out!? Please help

Answer 1

Hello, thank you for taking the time to post your question!

The key on this type of question is to use the information given in order to set up an algebraic expression.

On this one we have

x + y = 928   because there are 928 liters in total

0.08x + 0.24y = 0.12(928)   because when the 8% and 24% solutions are added together we need to have 928 Liters of 12% solution

From there then I would plug the first equation into the second and then solve algebraically for the value of x! When I do that I get x = 696, meaning that you need to add 696 L of the 8% solution in order to meet this criteria.

I hope that helps you get moving in a better direction on this type of question! Feel free to reach out if you have any additional questions beyond that :)

Answer 2

Lou:

 

You can do the problem in terms of 1 liter as follows:

 

Take a proportion alpha (of 1 liter) at 8% and a proportion (1 - alpha) (of 1 liter, adding to 1 liter total) at 24 %,  You want the overall proportion to be 12% in 1 liter.  You get

 

0.08 (alpha) + 0.24 (1 - alpha) = 0.12 (1)

 

This gives

 

0.16 (alpha) = 0.12 after a little re-arrangement.

 

That gives alpha = 12/ 16 = 3/4.

 

The above shows that you must take 3/4 = 75% of the 8% solution and remaining 25% should be the 24% solution to yield 12% solution OVERALL.  The total volume is 928 liters.  Divide it as

 

928 x 0.75  = 696 liters of 8%   (the answer you want)

 

and

 

928x 0.25 = 232 liters of 24% solution.

 

Dr. G.

 

 

Answer 3

make the table and start to fill it up, 

             solution * %(decimal) =   salt

(1)               x    *   0.08  =   0.08x

(2)          928-x  *   0.24  =   0.24(928-x)

----------------------------------------------------

(1)+(2)     928   *    0.12  =   111.36

 

Then use the value of salt,

  0.08x +  0.24(928-x) = 111.36

solve for x, then x = 696 liters.

Answer 4

let x=# of liters of an 8% solution

928-x=# of liters of a 24% solution

8%*x+(928-x)*24%=928*12%

0.08x+0.24(928-x)=0.12*928

0.08x+222.72-0.24x=111.36

-0.16x+222.72=111.36

-0.16x=111.36-222.72

-0.16x=-111.36

0.16x=111.36

16x=11,136

x=11,136/16

x=696 liters of an 8% solution

.08*696=55.68

0.24*(928-696)=0.24*232=55.68

0.12*928=111.36

55.68+55.68=111.36