Question 670719: You need a(n) 2% acid solution, and you'll get it by adding a(n) 10% acid solution to 25 liters of a(n) 1% acid solution. How many liters must be added? The amount of the 2% solution to be added is ? liters??
You need a(n) 5% acid solution, which you'll get by adding a(n) 16% acid solution to 21 liters of a(n) 3% acid solution. How many liters must be added?
The amount of the 16% solution to be added is ? liters.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! x + y = z
x number of liters of 10% solution
y = number of liters of 1% solution.
z = number of liters of 2% solution.
.10x + .01y = .02z
the 2 equations you need to deal with are:
x + y = z (number of liters of each solution)
.10x + .01y = .02z (number of liters of acid in each solution).
you know that y = 25 because that's given.
your formulas becomes:
x + 25 = z
.10x + .01(25) = .02z
from the first equation, solve for z to get z = x + 25
replace z with x + 25 in the second solution to get:
.10x + .01(25) = .02(x + 25)
solve for x in this equation.
simplify the equaton to get:
.10x + .25 = .02x + .5
subtract .02x from both sides of this equation and subtract .25 from both sides of this equation to get:
.10x - .02x = .5 - .25
simplify to get:
.08x = .25
divide both sides of this equation by .08 to get:
x = .25 / .08 = 3.125
you need to add 3.125 liters of a 10% solution to 25 liters of a 1% solution to get a 2% solution.
since y = 25 and x = 3.125, then z must be equal to 28.125
x + y = z becomes 3.125 + 25 = 28.125
.10x + .01y = .02z becomes:
.10(3.125) + .01(25) = .02(28.125)
simplify this to get:
.3125 + .25 = .5625 which becomes:
.5625 = .5625
numbers check out so the solution is good.
you get .5625 liters of acid in the combined solution which is 2% of 28.125 liters.
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