The amount Tom had left after drying and pickled the mushrooms needs to be first found.
5/5 - 2/5 = 3/5
9/9 - 5/9 = 4/9
Knowing that, the question can be reworded as:
Tom had 3/5 of the total amount of mushrooms left after drying them. Then, Tom had 4/9 of the previous amount of mushrooms he had left after pickling them. Finally, the remaining 28 mushrooms were fried, and none was left afterwards.
The equation that can be set up to answer the question (x = mushrooms gathered):
[tex] \frac{4}{9} ( \frac{3x}{5})-28=0 [/tex]
[tex] \frac{4}{9}( \frac{3x}{5})=28 [/tex]
[tex] \frac{12x}{45}=28 [/tex]
[tex]12x=1260[/tex]
[tex]x=105[/tex]
Tom gathered 105 mushrooms.
