Question

this year 75% of the graduating class had taken at least 8 math courses. of the remaining class members, 60% had taken 6 or 7 math courses.What % of the graduating class had taken fewer than 6 math courses?

Answer 1

suppose the total members of the class is x.
75% of x had taken at least 8 math courses.
that means the remaining had taken fewer than 8 courses.
the remaining class members is 100%x - 75%x = 25%x

then 60% of the remaning class members had taken 6 or 7 math courses . since the remaining class members is 25% , teh class member that had taken 6 or 7 math courses is:
60% of 25%x = (60/100)(25x/100) = 15x/100 = 15%x

so the class members that had taken fewer than 6 math courses is
25%x - 15%x = 10%x or 10% of the graduating class

Answer 2

10% have taken fewer than 6 math courses. It is calculated as follows: 60% of the remaining 25% = 15%, and 75% + 15% = 90% which leaves 10% of the students taking fewer than 6 math courses.