SOLUTION: a scientist wants to make a solution that is 30% acid using one solution that is 50 % acid and another solution that is 20% acid.How many liters of each solution does the scientis

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Question 708706: a scientist wants to make a solution that is 30% acid using one solution that is 50 % acid and another solution that is 20% acid.How many liters of each solution does the scientist need to make 75 liters of the mixture?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
v= known resulting volume, 75 liters
p%5B1%5D = low concentration material, 20%
p%5B2%5D = high concentration material, 50%
p%5Bt%5D = the target concentration of mixture, 30%
x = how much low concentration material to use
y = how much high concentration material to use

INITIAL SYSTEM
%28xp%5B1%5D%2Byp%5B2%5D%29%2Fv=p%5Bt%5D
x%2By=v

Work with and possibly do other simplifications to the percent-concentration equation,
%28xp%5B1%5D%2Byp%5B2%5D%29=vp%5Bt%5D

Use the volume sum equation to solve for either variable and substitute into the percentage equation and find the single variable there. As general example, solve for y:

x+y=v, y=v-x. Substitute.
%28xp%5B1%5D%2B%28v-x%29p%5B2%5D%29=vp%5Bt%5D, and solve for x
xp%5B1%5D%2Bvp%5B2%5D-xp%5B2%5D=vp%5Bt%5D
xp%5B1%5D-xp%5B2%5D=-vp%5B2%5D%2Bvp%5Bt%5D
x%28p%5B1%5D-p%5B2%5D%29=-vp%5B2%5D%2Bvp%5Bt%5D
x%28p%5B2%5D-p%5B1%5D%29=vp%5B2%5D-vp%5Bt%5D Equivalent to multiplying both sides by -1
x=v%28v%5B2%5D-p%5Bt%5D%29%2F%28p%5B2%5D-p%5B1%5D%29
And that would be the symbolic form for x, the lower concentration material. Just substitute the given values.