Answer
coffee $1.50$, juice $1.75$, and doughnut $0.75$ dollars
Work Step by Step
Step 1. Assume the price of coffee is $x$, of juice is $y$, and of doughnuts is $z$ dollars
Step 2. Based on the conditions given, set up the following system of equations:
$\begin{cases} 2x+y+2z=6.25\hspace2cm(Anne)\\x+3z=3.75\hspace3cm(Barry)\\3x+y+4z=9.25\hspace2cm(Cathy) \end{cases}$
Step 3. Subtract equation 1 from equation 3 to get $x+2z=3$
Step 4. Subtract the above equation from the middle one of the system of equations in step 2: $z=0.75$
Step 5. Find $x=3-2z=1.50$, and $y=6.25-2x-2z=1.75$
Step 6. Conclusion: the price of coffee is $1.50$, of juice is $1.75$, and of doughnuts is $0.75$ dollars
