A bottle holds 48 tsp of vanilla. The amount of A of vanilla remaining in the bottle decreases by 2 tsp per batch b of cookies.
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In both cases,
(as a consequence of the interesecting secant-tangent theorem)
So we have
10.
(omit the negative solution because that would make at least one of AB or AD have negative length)
11.
(again, omit the solutions that would give a negative length for either AB or AD)