You need 845 mL of a 75% alcohol solution. On hand, you have a 35% alcohol mixture. How much of the 35% alcohol mixture and pure alcohol will you need to obtain the desired solution?

Question

You will need

____ mL of the 35% solution

and

_____ mL of pure alcohol.

Answer 1

Let a = the amount of 35% solution that we will need

Let b = the amount of 100% pure alcohol that we will need

So we know that our solution equation is

(A) a + b = 845

And the amount of pure alcohol in the 75% solution is given by

(B) .35*a + 1.0*b = .75*845 = 633.75

We can subtract equation (B) from equation (A):

.65*a + 0*b = 211.25

And divide both sides by .65:

a = 325 ml of 35% solution

and

b = 845 - a = 520 ml of pure alcohol.

Answer 2

(35x+100y)/(x+y)=845/75%

=75x+75y=75%

40x=25y (like terms)

x=25, y=40

845/65=13

x= 13*25=325

y= " *40=520