SOLUTION: A chemist has two large containers of sulfuric acid solution, with different concentrations of acid in each container. Blending 200 mL of the first solution and 700 mL of the secon

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Question 1119968: A chemist has two large containers of sulfuric acid solution, with different concentrations of acid in each container. Blending 200 mL of the first solution and 700 mL of the second gives a mixture that is 14% acid, whereas blending 300 mL of the first mixed with 900 mL of the second gives a
14 1/2% acid mixture. What are the concentrations of sulfuric acid in the original containers?
Found 2 solutions by ikleyn, addingup:
Answer by ikleyn(52794)   (Show Source): You can put this solution on YOUR website!
.
The condition gives you this system of two equations in two unknowns


200x + 700y = 0.14 *(200+700)     (1)
300x + 900y = 0.145*(300+900)     (2)


where x is the concentration of the acid in the first  container (expressed as real number) and 

      y is the concentration of the acid in the second container.


Simplify and solve the system.


Answer by addingup(3677)   (Show Source): You can put this solution on YOUR website!
200x + 700y = 900(0.14)
300x + 900y = 1200(0.145
**************************
200x + 700y = 126 (1) multiply all sides times -1.5 and add to (2)
300x + 900y = 174 (2)
*****************************
300x + 900y = 174
+
-300x + -1050y = -189
----------------------
0x + -150y = -15; y = -15/-150 = 0.1 = 10%
The concentration of the second solution is 10%
****************************
200x + 700(0.1) = 126
200x + 70 = 126
200x = 56
x = 0.28
The concentration of the first solution is 28%
**********************
Let's see if this is true:
200x + 700y = 126; 200(.28) + 700(.1) = 126; 56 + 70 = 126 Correct
300x + 900y = 174; 300(.28)+ 900(.10) = 174; 84 + 90 = 174 Correct
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