A mixture of 6% disinfectant solution is to be made from

Question

A mixture of 6% disinfectant solution is to be made from 8% and 5% disinfectant solutions. How much of each solution should be used if 33 gallons of 6% solution are needed?

 

___ gallons of 8% solution

 

___ gallons of 5% solution 

Answer 1

the formula is C1V1 + C2V2 = C3V3 where C = concentration and V = volume

to simplify the process, we will change the % figures to decimals; 5% = 0.05, 6% = 0.06, 8% = 0.08

let x = volume of 8% solution, then 33g - x = volume of 6% solution

our equation becomes 0.08x + 0.05(33g - x) = 33g•0.06

expanding, we get 0.08x + 1.65g - 0.05x = 1.98g

combining, we get 0.03x = 0.33g

solving, x = 11g; then 33g - x = 22g

Proof: 0.08(11g) + 0.05(22g) = 0.06(33g); 0.88g + 1.1 = 1.98g