SOLUTION: You need 455 mL of a 85% 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 solut

Algebra ->  Inverses -> SOLUTION: You need 455 mL of a 85% 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 solut      Log On


   

Question 1162818: You need 455 mL of a 85% 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?
You will need ____ mL of the 35% solution and ______ mL of pure alcohol.
Answer by Edwin McCravy(20059) About Me  (Show Source):
You can put this solution on YOUR website!

I'll change the numbers so you'll have to do something other than type them
in and get credit for what somebody else did.
You need 605 mL of a 75% alcohol solution. On hand, you have a 45%
alcohol mixture. How much of the 45% alcohol mixture and pure alcohol will
you need to obtain the desired solution?
        |How many ml?|Strength| ml of pure alcohol
-------------------------------------------------
Solution|     x      | 0.45   |     0.45x
Alcohol |     y      | 1.00   |     1.00y
---------------------------------------------
            605        0.75         0.75(605) 

The equations come from the first and last columns:

             x + y = 605
     0.45x + 1.00y = 0.75(605)
    --------------------------

Multiply the second equation through by 100,
that is, move the decimal 2 places right on one factor:

             x + y = 605
        45x + 100y = 75(605)
    --------------------------

Multiply 75 times 605 get 45375

             x + y = 605
        45x + 100y = 45275
    --------------------------

Solve the first equation for x

                 x = 605 - y

Substitute that for x in the second equation

        45x + 100y = 45275
45(605 - y) + 100y = 45275
27225 - 45y + 100y = 45275
       27226 + 55y = 45275
               55y = 18150
                 y = 18150/55
                 y = 330 ml of pure alcohol

Substitute in

                 x = 605 - y
                 x = 605 - 330
                 x = 275 ml of mixture

Now do the same with your numbers.

Edwin