A mixture of 20% disinfectant solution is to be made from 13% and 23% disinfectant solution. How much of each solution should be used if 40 gallons of the 20% solution are needed?
If there are x gallons of 13%, then the rest (40-x) is 23%. So, adding up all the disinfectant, you have
.13x + .23(40-x) = .20*40
To find out how much of each solution should be used, let's break down the information provided:
Let's assume x gallons of the 13% disinfectant solution are used.
Therefore, the remaining (40 - x) gallons of the 23% disinfectant solution will be used to make up the 40-gallon mixture.
Now let's determine the amount of disinfectant in each solution:
For the 13% disinfectant solution:
Percentage of disinfectant = 13%
Therefore, the amount of disinfectant in x gallons of the 13% solution = (13/100) * x = 0.13x
For the 23% disinfectant solution:
Percentage of disinfectant = 23%
Therefore, the amount of disinfectant in (40 - x) gallons of the 23% solution = (23/100) * (40 - x) = 0.23 * (40 - x) = 9.2 - 0.23x
Now, the total amount of disinfectant in the mixture should be 20% of 40 gallons:
Percentage of disinfectant = 20%
Therefore, the total amount of disinfectant in the mixture = (20/100) * 40 = 0.2 * 40 = 8
Now we can set up an equation using the amounts of disinfectant in each solution:
Amount of disinfectant in the 13% solution (0.13x) + Amount of disinfectant in the 23% solution (9.2 - 0.23x) = Total amount of disinfectant in the mixture (8)
0.13x + 9.2 - 0.23x = 8
Now let's solve the equation:
0.13x - 0.23x = 8 - 9.2
-0.1x = -1.2
x = (-1.2)/(-0.1)
x = 12
Therefore, you should use 12 gallons of the 13% disinfectant solution and (40 - 12) = 28 gallons of the 23% disinfectant solution to make 40 gallons of a 20% disinfectant solution.