Let the common ratio be $x$. Then we have $16x+9x=25x$ buns and pies to begin with. After selling $192$ buns and pies, $16x+9x-192$ buns and pies are left. We know that $\frac{1}{3}$ of the remaining $9x$ pies are left, so $\frac{2}{3}$ of the pies were sold. That means $\frac{2}{3}(9x)=6x$ pies were sold, leaving $9x-6x=3x$ pies remaining.
Also, the number of buns decreased by $\frac{3}{8}(16x)=6x$. Since we still have a ratio of $16:9$, we know that $9x$ buns were sold. Thus, we have the equation \begin{align*}
16x-6x &= 9x \\
\Rightarrow \qquad x &= 3.
\end{align*}
So, the original number of buns and pies was $16(3)=48$ and $9(3)=27$, respectively. Then, $48+27=75$ buns and pies were sold, leaving $16(3)-6(3)=30$ buns and $9(3)-3=24$ pies. Chandra bought $\frac{3}{4}(24)=18$ pies at $3.85 each, so she paid $18(3.85)=\boxed{\$69.30}$.
Amy had some buns and pies in the ratio 16: 9. After she sold a total of 192 buns and pies, 1/3 of the pies were left and the number of buns decreased by 3/8. Chandra bought 3/4 of Amy's remaining pies at
$3.85 each.
(a) How many buns were sold?
(b) How much money did Chandra pay for the pies?
.
1 answer