Roberto needs to produce 2000 milliliters of 55% alcohol solution.

Question

Roberto needs to produce 2000 milliliters of 55% alcohol solution. At his disposal he has 20% alcohol solution and 60% alcohol solution. How much of each does he need in order to produce his desired solution?

 

He needs _____milliliters of 20% solution.
He needs _____milliliters of 60% solution

Answer 1

X is the amount of 20 proof

Y is the amount of 60 proof

20% is 0.2 , 55% = 0.55, and 60% = 0.6

 

 

The amount of alcohol is:

 

    0.2X + 0.6Y = 0.55*2000 mL

 

   0.2X + 0.6Y = 1100 mL

    2X + 6Y = 11000 mL  <--- multiplies everything by 10 to clear the decimals

 

  X + Y = 2000 ---> y = 2000 - x

 

  2X + 6(2000 - x) = 11000

 2x + 12000 - 6x = 11000

 

 0 = 11000 + 6x - 12000 - 2x

 

  0 =  4x - 1000

 

1000 = 4x

 

x = 250

 

y = 1750

 

 

He needs   250 milliliters of the 20% solution.

He needs 1750 milliliters of the 60% solution.