SOLUTION: How many liters of a 10% alcohol solution must be mixed with 70 liters of a 90% solution to get a 30% solution? Thanks in advance for your help!

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Question 155666: How many liters of a 10% alcohol solution must be mixed with 70 liters of a 90% solution to get a 30% solution?
Thanks in advance for your help!
Found 2 solutions by jojo14344, Earlsdon:
Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!
There are 2 unknowns in the problem: VOLUME OF ALCOHOL ---> A%28Liters%29? VOLUME OF OUTPUT SOLUTION---> S%5B2%5D%28Liters%29?
We'll go to the 1st condition: 10% of Alcohol mixed with 90% of 70L of initial solution S%5B1%5D to produce 30% of S%5B2%5D. To show:
0.10A%2B70L%280.90%29=0.30S%5B2%5D
0.10A%2B63L=0.30S%5B2%5D ----------------------> eqn 1
Now, when we add the Volume of A and S%5B1%5D, we get the volume of S%5B2%5D. To show:
A%2BS%5B1%5D=S%5B2%5D --------------------------------> eqn 2
Continuing, A%2B70L=S%5B2%5D ---------------------> eqn 3
Substitute eqn 3 in eqn 1:
0.10A%2B70L%280.90%29=0.30%28A%2B70L%29
0.10A%2B63L=0.30A%2B21L
63L-21L=0.30A-0.10A
42L=0.20A -----> cross%2842L%29210L%2Fcross%280.20%29=cross%280.20%29A%2Fcross%280.20%29
A=210L -------------------> volume of Alcohol
: For Volume of S%5B2%5D, go back eqn 2:
210L%2B70=S%5B2%5D
S%5B2%5D=280L -------------------> volume of output solution
In doubt? go back eqn 1:
0.10%28210%29%2B70%280.90%29=0.30%28280%29
21%2B63=84
84L=84L
thank you
Jojo

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = the number of liters of 10% alcohol solution to be added to 70 liters of 90% alcohol solution to get (x+70) liters of 30% alcohol solution.
After changing the percentages to their decimal equivalents, we can express this as:
(0.1)x + (0.9)(70) = (x+70)(0.3) Simplify this and solve for x.
0.1x+63 = 0.3x+21 Subtract 0.1x from both sides.
63 = 0.2x+21 Subtract 21 from both sides.
42 = 0.2x Finally, divide both sides by 0.2
x = 210 liters.
You would need to mix 210 liters of a 10% alcohol solution to 70 liters of 90% alcohol solution to obtain 280 (210+70) liters of 30% alcohol solution.