Problem: In a class of 40 students the number of students who study French is 10 more than the number of students who study history. If 8 students study both subjects, how many students study French and how many study history? 1. Let the number of students who study history be $H$. 2. Then the number who study French is $F=H+10$. 3. The number of students who study at least one of the two subjects equals $F+H-8$ because 8 students are counted in both groups. 4. We assume every student studies at least one of the two subjects, so $F+H-8=40$. 5. Substitute $F$ into the equation: $(H+10)+H-8=40$. 6. Simplify the left side to get: $$2H+2=40$$ 7. Solve for $H$: $$2H=38$$ 8. $$H=19$$ 9. Then $F=H+10=29$. 10. Final answer: 29 students study French and 19 students study history.