起初，达莉亚比胡达多 30 张贴纸。达莉亚将自己 40% 的贴纸给了胡达。接着，胡达将自己 50% 的贴纸给了达莉亚。最后，达莉亚比胡达多 48 张贴纸。达莉亚起初有多少张贴纸？

1. Define variables for the initial number of stickers

Let Dalia's initial number of stickers be $D$ and Huda's be $H$.

2. Express the number of stickers each has after Dalia gives 40% to Huda

Dalia gives $40\%$ of her stickers to Huda.
Dalia has $100\% - 40\% = 60\%$ of her stickers left, which is $0.6D$.
Huda receives $0.4D$, so Huda now has $H + 0.4D$.

3. Express the number of stickers each has after Huda gives 50% to Dalia

Huda gives $50\%$ (half) of her current stickers to Dalia.
Huda gives $0.5(H + 0.4D) = 0.5H + 0.2D$.
Huda is left with $0.5H + 0.2D$.
Dalia receives this amount, so Dalia now has $0.6D + 0.5H + 0.2D = 0.8D + 0.5H$.

4. Use the final difference to form an equation and solve for Dalia's initial stickers

In the end, Dalia has 48 more stickers than Huda.
$(0.8D + 0.5H) - (0.5H + 0.2D) = 48$
$0.6D = 48$
$D = \frac{48}{0.6} = 80$
(Note: The initial difference of 30 is extra information not needed to find Dalia's initial amount.)