When a group of students are seated 3 to a bench in an auditorium, 18 are left standing. If they were seated 4 to a bench, 3 benches would be empty. Find the number of benches and students

x = students

b = benches

when 3 are on a bench and 18 are standing the equation is:

x = 3b+18

when 4 are sitting and 3 benches are empty the formula is

and x = 4b-12

so 3b+18 = 4b-12

rearrange to

4b-3b = 18 + 12

so b = 30

now plug that into the first formula

x=3 (30) + 18 = 108

so 108 students and 30 benches