Ahmad spent 2/5 of his money on 15 burgers and 75 cupcakes for a party. The cost of each cupcake is 1/3 the cost of each burger. He bought some more burgers with 4/5 of his remaining money.
(a) How many cupcakes could be bought with the same amount of money paid for the 15 burgers?
(b) How many burgers did Ahmad buy altogether?
+179 $(a)$
Since each burger costs 3 times that of a cupcake, naturally it follows that $15 \cdot 3 = \boxed{45}$.
$(b)$
Let the cost of a burger be $x$. Writing an equation gives $15x + \frac{75}{3}x = 40x$, for the number of burgers Ahmad could buy with $\frac{2}{5}$ of his total money. $\frac{3}{5} \cdot \frac{4}{5} = \frac{12}{25}$, meaning that $\frac{4}{5}$ of his remaining money is $\frac{12}{25}$ of his total money.
We can see that $\frac{2}{5} \cdot 1.2 = \frac{12}{25}$, meaning that he brought $40 \cdot 1.2 = 48$ burgers with his remaining money.
Adding the burgers from before together gives $15 + 48 = \boxed{63}$ burgers in total.
