Answer
chemical engineering majors $22$,
mathematics majors $16$,
psychology majors $14$.
Work Step by Step
Step 1. Add the hours for chemical engineering $x$, mathematics $y$, and psychology $z$; we have $x+y+z=52$
Step 2. Subtracting the hours of math from chemical engineering, we have $x-y=6$
Step 3. Subtracting the hours of psychology from chemical engineering, we have $x-z=8$
Step 4. Adding the first two equations, we have $2x+z=58$
Step 5. Adding the equation of steps 3 and 4, we have $3x=66$, which gives $x=22$ hours.
Step 6. Back substitute the known values to get $y=16$ hours, and $z=14$ hours.
Step 7. We conclude that the average number of hours per week are:
chemical engineering majors $22$, mathematics majors $16$, and psychology majors $14$.
