SOLUTION: can you help with this problem: ten gallons of a 30% acid mixture is obtained by mixing a 20% solution with a 50% solution. How much of each must be used? i've tried creating

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: can you help with this problem: ten gallons of a 30% acid mixture is obtained by mixing a 20% solution with a 50% solution. How much of each must be used? i've tried creating      Log On


   

Question 176462: can you help with this problem:
ten gallons of a 30% acid mixture is obtained by mixing a 20% solution with a 50% solution. How much of each must be used?
i've tried creating two linear equations (one for total volume and one for concentration) but i don't know where to go from there.
Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
ok lets call the amount of 20% and 50% solutions a and b respectively
:
a+b=10...........eq 1
.2a+.5b=.3(10)...eq 2
:
rewrite eq 1 to a=10-b and plug this value into eq 2
:
.2(10-b)+.5b=3
:
2-.2b+.5b=3
:
.3b=1
:
highlight%28b=3.33%29amount of 50% solution
:
highlight%28a=10-b=10-3.33=6.67%29amount of 20% solution