Answer
The average number of hours per week are:
physics $20$, English $16$, and sociology $14$.
Work Step by Step
Step 1. Add the hours for physics $x$, English $y$, and sociology $z$: $x+y+z=50$
Step 2. Subtracting the hours of English from physics, we have $x-y=4$
Step 3. Subtracting the hours of sociology from physics, we have $x-z=6$
Step 4. Adding the first two equations, we have $2x+z=54$
Step 5. Adding the equation of steps 3 and 4, we have $3x=60$, which gives $x=20$ 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:
physics $20$, English $16$, and sociology $14$.
