In summer squash, fruit colour is controlled by two genes, $A$ and $B$, which assort independently on different autosomes. The dominant allele $A$ results in white fruit, masking the expression of the $B$ gene (dominant epistasis). In homozygous recessive $aa$ individuals, the dominant allele $B$ produces yellow fruit, while the homozygous recessive genotype $aabb$ produces green fruit.

A geneticist crosses two double heterozygous ($AaBb$) plants and obtains a total of 480 offspring in the $F_2$ generation. Assuming the offspring phenotypes perfectly fit the expected ratio for dominant epistasis, how many of these offspring are expected to have yellow fruit?