A custodian is going to mix a 4% ammonia solution and a 12% ammonia solution to get 1 gallon (128 fluid ounces) of a 9% ammonia solution. How many fluid ounces of the 4% solution and the 12% solution should be used?

Aug 23, 2015

$48$ ounces of 4% solution and $80$ ounces of 12% solution will give $128$ ounces of 9% solution.

Explanation:

Let the number of ounces of 4% solution be $k$
$\rightarrow$ the number of ounces of 12% solution must be $128 - k$

$4 k + 12 \left(128 - k\right) = 9 \left(128\right)$

$4 k + 1536 - 12 k = 1152$

$- 8 k = - 384$

$k = 48$
$48$ ounces of 4% solution and
$128 - 48 = 80$ ounces of 12% solution