Track the remaining percentage after each purchase.
\\(\begin{aligned}
\text{After sandwich (25\%)} &: 75\% \text{ remaining}
\\
\text{Juice: 40\% of 75\%} &= 30\% \text{ of original}
\\
\text{After juice} &: 75\% - 30\% = 45\% \text{ remaining}
\\
\text{Cookie: 50\% of 45\%} &= 22.5\% \text{ of original}
\\
\text{After cookie} &: 45\% - 22.5\% = 22.5\% = \$13.50
\\
\text{Original} &= \$13.50 \div 0.225 = \$60
\end{aligned}\\)
Final Answer: \$60