Question

Challenge An arts academy requires there to be 6 teachers for every 138 students and 5 tutors for

every 40 students. How many students does the academy have per teacher? Per tutor? How many
tutors does the academy need if it has 104 students?

Answer 1

To find the number of students per teacher, set up a proportion. To find the number of students per tutor, use the same method. To find the number of tutors needed for 104 students, use the tutor-to-student proportion.

Step-by-step explanation:

To find the number of students per teacher, we can set up a proportion. We know that there are 6 teachers for every 138 students, so we can set up the proportion: 6 teachers / 138 students = x teachers / y students. Cross-multiplying, we get: 6y = 138x. To find the number of students per tutor, we can use the same method. We know that there are 5 tutors for every 40 students, so the proportion becomes: 5 tutors / 40 students = x tutors / y students. Cross-multiplying, we get: 5y = 40x. To find the number of tutors needed for 104 students, we can use the tutor-to-student proportion: 5 tutors / 40 students = x tutors / 104 students. Cross-multiplying, we get: 5 * 104 = 40x. Solving for x, we get: x = 13 tutors.