Question

There are x benches and y students in an auditorium. When a bench is seated with 3 students, 18 are left standing. If a bench is seated with 4 students, 3 benches would be empty.

a. Write 2 equations showing the relationship between x benches and y students
b. Find the number of benches and students

Answer 1

x- benches, y-students

`y=3x+18\\x-3=(y)/(4)`

`x=(y)/(4)+3 \\ \\y=3((y)/(4)+3)+18 \\ \\y= (3y)/(4) +9+18 \\ \\4y=3y+36+72 \\y=108 \\ \\x= (108)/(4) +3=27+3=30`