There are 35 students in David's homeroom class. There are 5 students who take English and Biology,and 7 students who take neither of these subjects.There are 3 more students taking English only than there are students taking biology only. The number of students in David's homeroom class who take English only is?
my work:
35 students in Davids homeroom 5 students take English and biology 7 students take neither subjects 3 more take English than there are taking biology
5+7=12-3=9 students who take English only
is this the correct way to solve it,if not whats a correct solution to solve this question?
The total number of students is $35$ and $35-7=28$ students are taking at least one class. $28-5=23$ students are taking only one class. $23$ students are taking ONLY Biology or ONLY English: $23=B+E \implies 23=B+B+3 \implies B=10$. Therefore, $13$ students take ONLY English. $13+5=\boxed{18}$ students take English as a class.