Final answer:
To find the number of students who answered 'yes' out of 2911 students given the ratio of 'yes' : 'no' : 'undecided', set up a proportion and solve for the count of 'yes' students.
Step-by-step explanation:
To find the number of students who answered 'yes' out of the total 2911 students, we need to find the number that corresponds to the 'yes' ratio. The given ratio is 51 : 7 : 13 for 'yes' : 'no' : 'undecided'.
To find the number of students who answered 'yes', we can set up a proportion:
'yes' ratio / total students = 'yes' count / total students
51 / (51 + 7 + 13) = 'yes' count / 2911
51 / 71 = 'yes' count / 2911
Now, we can solve for 'yes' count:
'yes' count = (51 / 71) * 2911
'yes' count ≈ 2070.96
Therefore, approximately 2071 students answered 'yes'.