In conclusion, there are 9 students per tutor. To accommodate 99 students, the academy would need to round up to 12 tutors. The cost of attending the academy can be expressed in an equation, T = $500 + ($3,000 * number of years).
To determine the number of students per teacher and per tutor, as well as the number of tutors needed for a given number of students, we can use ratios and proportions. The question states that for every 36 students, there are 4 tutors. First, we find the ratio of students to tutors, which is 36 students to 4 tutors, or 9 students per tutor when simplified.
Then, to find the number of tutors needed for 99 students, we set up a proportion: 36 students / 4 tutors = 99 students / x tutors. Solving for x, we get x = (99 students * 4 tutors) / 36 students = 11 tutors. However, since we cannot have a fraction of a tutor, we round up to the nearest whole number, which is 12 tutors.
To provide an equation for the cost associated with enrolling in the school, we use the given figures: a one-time enrollment fee of $500, plus $3,000 per year for tuition. The total cost (T) can be expressed as T = $500 + ($3,000 * number of years).