Answer:
90/19
Explanation:
Since the ratio of gooseberry juice to mooseberry juice in Bottle A is $2:3,$ we know that $\dfrac{2}{2+3}=\dfrac{2}{5}$ of the juice is gooseberry juice, and $\dfrac{3}{2+3}=\dfrac{3}{5}$ of the juice is mooseberry juice. Therefore, there are $\dfrac{2}{5} \cdot 45=18$ ounces of gooseberry juice and $\dfrac{3}{5} \cdot 45=27$ ounces of mooseberry juice in Bottle A.
Now, suppose that Bottle B had $x$ ounces of juice. Since the ratio of gooseberry juice to mooseberry juice in Bottle B is $7:3,$ it follows that $\dfrac{7}{7+3}=\dfrac{7}{10}$ of the juice is gooseberry juice, and $\dfrac{3}{7+3}=\dfrac{3}{10}$ of the juice is mooseberry juice. Therefore, Bottle B had $\dfrac{7x}{10}$ ounces of gooseberry juice and $\dfrac{3x}{10}$ ounces of mooseberry juice.
When the two bottles of juice are combined, the total volume of juice will be $45+x$ ounces. Since the ratio of gooseberry juice to mooseberry juice here is $3:4,$ it follows that $\dfrac{3}{3+4}=\dfrac{3}{7}$ of this is gooseberry juice, so there must be a total of $\dfrac{3}{7} \cdot (45+x)=\dfrac{135}{7}+\dfrac{3x}{7}$ ounces of gooseberry juice among both bottles. However, we know that there are $18$ ounces of gooseberry juice in Bottle A and $\dfrac{7x}{10}$ ounces of gooseberry juice in Bottle B, so it follows that
\[\dfrac{135}{7}+\dfrac{3x}{7}=18+\dfrac{7x}{10}.\]Subtracting $18$ and $\dfrac{3x}{7}$ from both sides of this equation, we get $\dfrac{9}{7}=\dfrac{19x}{70}.$ Multiplying both sides of the equation by $70,$ we get $90=19x.$ Dividing both sides of the equation by $19,$ we get $x=\dfrac{90}{19}.$ Since we defined $x$ to be the number of ounces of juice in Bottle B, it follows that Bottle B has $\boxed{\dfrac{90}{19}}$ ounces of juice.