Question 670719
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.