Question 224231
 The concentrations of the acid is different in the two containers.
 He blends 10 mL of the first solution with 90 mL of the second solution to obtain a solution that is 15.15.% acid.
 He blends 100 mL of the first solution with 150 mL of the second solution to obtain a solution that is 15.60.% acid.
 What are the concentrations of hydrochloric acid in the original containers?
:
Use decimal equiv of the percent;
:
Let x = acid concentration of the 1st container
Let y = acid concentration of the 2nd container
:
"He blends 10 mL of the first solution with 90 mL of the second solution to obtain a solution that is 15.15.% acid."
10x + 90y = .1515(100); resulting amt is the sum of the two solutions
10x + 90y = 15.15
:
"He blends 100 mL of the first solution with 150 mL of the second solution to obtain a solution that is 15.60.% acid."
100x + 150y = .1560(250)
100x + 150y = 39
Simplify, divide by 10
10x + 15y = 3.9
:
Subtract this from the 1st equation:
10x + 90y = 15.15
10x + 15y = 3.9
--------------------subtraction eliminate x, find y
75y = 11.25
y = {{{11.25/75}}}
y = .15 or 15% is the concentration of the 2nd container
:
find x using equation: 10x + 15y = 3.9
10x + .15(15) = 3.9
10x + 2.25 = 3.9
10x = 3.9 - 2.25
10x = 1.65
x = {{{1.65/10}}}
x = .165 or 16.5% is the concentration of the 1st container
:
:
Check solution in the statement:
He blends 100 mL of the first solution with 150 mL of the second solution to obtain a solution that is 15.60.% acid."
.165(100) + .15(150) = .156(250)
16.5 + 22.5 = 39
39 = 39