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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?

Aug 2, 2021

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$(a)$

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.

Aug 2, 2021