Candy Box Dilemma

Question

There was a box of candy on the table. Ali ate half the candy. Miranda came along and took two-thirds of it. Jane decided she wanted some, so she took three-fourths of the remaining candy. Micayla took one piece and Alejandro took the last single piece. How many pieces of candy were there to begin with?

Answer 1

let box have M candy.

ali ate half , so it remains $\frac{M}{2}$

miranda took $\frac{2}{3}$ from $\frac{M}{2}$, so it remains $\frac{1}{3}$ from $\frac{M}{2}$ and that is $\frac{M}{6}$

jane took $\frac{3}{4}$ from $\frac{M}{6}$ , so it remains $\frac{1}{4}$ from $\frac{M}{6}$ and that is $\frac{M}{24}$

micayla and alejandro took one each so $\frac{M}{24}=2$

from there you get $M=48$

Answer 2

There was 1 piece when Alejandro came along, so there were 2 pieces when Micayla stopped by, so there were $4\times2=8$ pieces when Jane stocked up (she took three-fourths, so what was left after she acted was one-fourth of what she found, so what she found was four times what she left for Micayla to find, so, 8). There were three times that many, so, $24$ pieces when Miranda stuffed her face, so $48$ pieces when Ali set to work.