SOLUTION: A chemist has three different acid solutions. The first acid solution contains 25% acid, the second contains 40% and the third contains 85%. He wants to use all three solutions to

Question 1156055: A chemist has three different acid solutions. The first acid solution contains 25% acid, the second contains 40% and the third contains 85%. He wants to use all three solutions to obtain a mixture of 72 liters containing 55% acid, using 2 times as much of the 85% solution as the 40% solution. How many liters of each solution should be used?
Found 3 solutions by greenestamps, Theo, josgarithmetic:
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

Let x = liters of 40% acid
then 2x = liters of 85% acid (twice as much as the 40%)
and 72-3x = liters of 25% acid (the rest to make a total of 72 liters)

The acid in those three equals 55% of the total 72 liters:

ANSWER:
40% acid: x = 16 liters
85% acid: 2x = 32 liters
25% acid: 72-3x = 24 liters

CHECK:
.40(16)+.85(32)+.25(24) = 6.4+27.2+6 = 39.6

Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
x = number of liters of 25% solution.
y = number of liters of 40% solution.
z = number of liters of 85% solution.
he wants 72 liters of 55% solution.
you have two equations that need to be solved simultaneously.
first is x + y + z = 72
second is .25 * x + .40 * y + .85 * z = .55 * 72
he wants to use 2 times as much of the 85% solution as the 40% solution.
this makes the third equation be z = 2 * y
you now have three equations that need to be solved simultaneously.
they are:
first equation is x + y + z = 72
second equation is .25 * x + .40 * y + .85 * z = .55 * 72
third equation is z = 2 * y
use the third equation to replace z with 2 * y in the first two equations.
first two equations becomes:
x + y + 2 * y = 72
.25 * x + .40 * y + .85 * 2 * y = .55 * 72
simplify and combine like terms to get:
x + 3 * y = 72
.25 * x + 2.1 * y = 39.6
multiply both sides of the first equation by .25 and leave the second equation as is to get:
.25 * x + .25 * 3 * y = .25 * 72
.25 * x + 2.1 * y = 39.6
simplify to get:
.25 * x + .75 * y = 18
.25 * x + 2.1 * y = 39.6
subtract the first equation from the second to get:
1.35 * y = 21.6
solve for y to get:
y = 21.6 / 1.35 = 16
since z = 2 * y, then z = 32
since x + y + z = 72, then x = 72 - 32 - 16 = 24
you now have:
x = 24
y = 16
z = 32
first original is true because they all add up to 72.
second original equation is:
.25 * x + .40 * y + .85 * z = .55 * 72
it becomes:
.25 * 24 + .40 * 16 + .85 * 32 = .55 * 72
simplify to get:
6 + 6.4 + 27.2 = 39.6
combine like terms to get:
39.6 = 39.6
this confirms the values of x, y, and z are good.
your solution is:
24 liters of 25% solution and 16 liters of 40% and 32 liters of 85% will give you 72 liters of 55% solution.
to confirm, do the following:
24 * .25 + 16 * .40 + 32 * .85 = 39.6
39.6 / 72 = .55 = 55%.

Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!

CONC.% VOLUME LITERS PURE ACID 25 x 0.25x 40 y 0.4y 85 2y 1.7y 55 72 0.55*72=39.6

You can have two equations.

They are equivalently

Their difference gives

and you can easily evaluate the other acid solution volumes.
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