Question

A mixture of
12%
disinfectant solution is to be made from
10%
and
17%
disinfectant solution. How much of each solution should be used if
28
gallons of the
12%
solution are needed?

Answer 1

Set up a system of 2 equations.
Gallon equation:
x+y = 28
Solution equation:
10x + 17y = (28)(12)

Solve with substitution:
y = 28-x  (From 1st equation)

(Sub into 2nd equation)
10x + 17(28-x) = 336

10x + 476 - 17x = 336

-7x = -140

x = 20

y = 28-20 = 8

Therefore the solution is (20,8)
You need 20 gal of 10% solution mixed with 8 gal of 17% solution to obtain 28 gal of 12% solution.