Problema Solution
Gerry Gundersen mixes different solutions with concentrations of 25%, 40% and 50% to get 200 liters of a 32% solution. If he uses twice as much of the 25% solution as of the 40% solution, find how many liters of each kind he uses.
Answer provided by our tutors
Volume of 40% solution = X
Volume of 25% solution = 2X
Volume of 50% solution = Y
3X + Y = 200 litres.
Overall concentration of the 25%-40% mix will be:
(2 x 0.25 + 1 x 0.4)/3 = 0.3 = 30%
Because the fluids are in ratio of 2:1, that solution will be constant at 30%, no matter what volume is used.
Now, to get the actual amounts right:
(3X x 0.3 + Y x 0.5) = 0.32
By rearranging the first formula to get 3X = 200 - Y, we get:
([200 - Y] x 0.3 + Y x 0.5) = 0.32 x 200
60 - 0.3Y + 0.5Y = 64
0.2Y = 64 - 60
0.2Y = 4 litres
2Y = 40 litres
Y = 20 litres
3X + Y = 200
X = (200 - 20)/3
X = 60 litres
So:
25% solution = 2X = 120 litres
40% solution = X = 60 litres
50% solution = Y = 20 litres.