Explain why the ratio 2 to 5 is different from the ratio 5 to 2 if they both represent the ratio of cats to dogs.

The ratio 2 to 5 means there are 2 cats and 5 dogs but the 5 to 2 ratio means there are 5 cats and 2 dogs.

Her conclusion that 90% of the student body wants the colors changed is an INCORRECT conclusion. The 90% out of 100% is not referring to the total numbers of the student body.For example, 100 people are members of student body if only 50 members responded the survey, then we have:
 90% of 50 members who answered the survey said that they want the changed.