Pre Cal Math Help!!!

Question

A chemist has two large containers of sulfuric acid solution, with different concentrations of acid in each container. Blending 310 mL of the first solution and 590 mL of the second gives a mixture that is 10.82% acid, whereas blending 80 mL of the first mixed with 485 mL of the second gives a 7.98% acid mixture. What are the concentrations of sulfuric acid in the original containers? (Round your answer to the nearest whole number.)

Answer 1

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

The key on this type of question is to use the underlying information in order to set up equations we can use to model the situation. So the two equations we get here are:

310C1 + 590C2 = 97.38        

80C1 + 485C2 = 45.087        

In that representation I’m using C1 to represent the concentration of sulfuric acid in the first container and C2 to represent the concentration of sulfuric acid in the second container. Then the 97.38 and 45.087 are the amount of acid in each mixture, found by taking (310 + 590) x 10.82% = 97.38 and  (80 + 485) x 7.98% = 45.087

Once you have a system of equations like that there are a variety of ways to solve! You could solve those using substitution, elimination, or something like an online system of equations calculator! Whatever approach that you use it should end up being

C1 = 20%

C2 = 6%, meaning that the concentration of the first container is 20% and the concentration of the second container is 6%.

I hope that helps get you moving in the right direction! Feel free to reach out if you have any additional questions beyond that :)

Answer 2

Let concentration of acid in first container be x%

and concentration of acis in second container be y%

 

x/100(310)  + y/100(590) = 10.82/100(310+590)  => 310x + 590y = 9378

x/100(80)  + y/100(485) = 7.89/100(80+485)        => 80x + 485y = 4458

 

solve two simultaneous equations to find x and y