SOLUTION: Gabe​ Amodeo, a nuclear​ physicist, needs 80 liters of a 30​% acid solution. He currently has a 20 % solution and a 60 % solution. How many liters of each does he need to m

Algebra ->  Customizable Word Problem Solvers  -> Mixtures -> SOLUTION: Gabe​ Amodeo, a nuclear​ physicist, needs 80 liters of a 30​% acid solution. He currently has a 20 % solution and a 60 % solution. How many liters of each does he need to m      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


   



Question 1159360: Gabe​ Amodeo, a nuclear​ physicist, needs 80 liters of a 30​% acid solution. He currently has a 20 % solution and a 60 % solution. How many liters of each does he need to make the needed 80 liters of 30​% acid​ solution?
Found 3 solutions by mananth, josgarithmetic, greenestamps:
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!

---------------- percent ---------------- quantity
Solution I 20% ---------------- x L
Solution II 60% ---------------- 80 - x L
Mixture 30.00% ---------------- 80
component percent ---------------- quantity
Solution I 0.2 ---------------- x L
Solution II 0.6 ---------------- 80 - x L
Mixture 0.30 ---------------- 80

0.2 x + 0.6 ( 80 - x ) = 80.00 * 0.30

0.2 x + 48 - 0.6 x = 24.00
0.2 x - 0.6 x = 24 - 48
-0.4 x = -24
/ -0.4
x = 60
20.00% Solution I =60L

60.00% Solution II 20 L




Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
---------------------------------
needs 80 liters of a 30​% acid solution. He currently has a 20 % solution and a 60 % solution.
--------------------------------

v of 60%
80-v of 20%

60v%2B20%2880-v%29=30%2A80
60v-20v%2B20%2A80=30%2A80
%2860-20%29v=30%2A80-20%2A80
highlight%28v=80%28%2830-20%29%2F%2860-20%29%29%29 and you can continue from here.
.
.

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


A fast and easy non-algebraic way of solving mixture problems like this....

(1) 30% is 1/4 of the way from 20% to 60%. (20 to 60 is 40; 20 to 30 is 10; 10/40 = 1/4)

(2) Therefore, 1/4 of the mixture is the 60% solution.

He needs 80L of the mixture; so 20L of the 60% solution and the remaining 60L of the 20% solution.

CHECK:
.60(20)+.20(60) = 12+12 = 24
.30(80) = 24