Precalculus (6th Edition) Blitzer

chemical engineering majors $22$, mathematics majors $16$, psychology majors $14$.
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 $14$.