Question

A mixture of 16 % disinfectant solution is to be made from 14 % and 22% disinfectant solutions. How muchof each solution should be used if 32 gallons of the 16 % solution are needed?There needs to be___gallons of 14% solution and___gallons of 22 % solution.

Answer 1

there need to be 24 gallons of disinfectant containing 14% solution and 8 gallons of disinfectant containing 22% solution

Step-by-step explanation:

let the amount of disinfectant containing 14% = x

let the amount of disinfectant containing 22% = y

The sum of the amount of both concentration gives the amount for the 16% concentration

Amount used for disinfectant containing 16% = 32 gallons

So, x + y = 32 gallons

x + y = 32 ....(1)

The amount from each concentration used:

14% (amount of this disinfectant used) + 22%(amount of this disinfectant used) = 16% (amount of this disinfectant used

14%(x) + 22%(y) = 16%(32)

0.14(x) + 0.22(y) = 0.16(32)

0.14x + 0.22y = 5.12 ....(2)

combining both equations:

x + y = 32 ....(1)

0.14x + 0.22y = 5.12 ....(2)

Using substitution method:

From equation (1), we can make x the subject of formula:

x = 32 - y

substitute for x in equation (2):

0.14(32 - y) + 0.22y = 5.12

0.14(32) - 0.14y + 0.22y = 5.12

4.48 - 0.14y + 0.22y = 5.12

4.48 + 0.08y = 5.12

0.08y = 5.12 - 4.48

0.08y = 0.64

divide both sides by 0.08:

y = 0.64/0.08

y = 8

substitute for y in equation (1)

x + 8 = 32

x = 32 - 8

x = 24

To get the 16% concentration, there need to be 24 gallons of disinfectant containing 14% solution and 8 gallons of disinfectant containing 22% solution