SOLUTION: A lab tech needs to make a 10 liter batch of antiseptic that is 60% alcohol. How can she combine a batch of 30% alcohol with another that is 70% to make the desired concentration?

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Question 178652This question is from textbook introductory and intermediate algebra
: A lab tech needs to make a 10 liter batch of antiseptic that is 60% alcohol. How can she combine a batch of 30% alcohol with another that is 70% to make the desired concentration?
This is in my section on systems of equations. I'm supposed to write a system of equations to solve this problem. I can't figure out how to make a system for this. Can someone please explain how to make a system for this? This question is from textbook introductory and intermediate algebra

Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
ok lets call the amount of 30% and 70% batch a and b respectively
:
x+y=10............eq 1 because there is 10 liters altogether
:
.3x+.7y=.6(10)....eq 2
:
rewrite eq 1 to x=10-y and plug that value into eq 2
:
.3(10-y)+.7y=.6(10)
:
3-.3y+.7y=6
:
.4y=3
:
highlight%28y=7.5%29liters of 70% batch
:
highlight%28x=10-7.5=2.5%29liters of 30% solution