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?

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Answer 1 · 2015-08-23T19:03:03

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

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

$4 k + 12 (128 - k) = 9 (128)$ $4k + 12(128-k) = 9(128)$

$4 k + 1536 - 12 k = 1152$ $4k + 1536 -12k = 1152$

$- 8 k = - 384$ $-8k = -384$

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