Question

A daycare center is determining the number of toddler and preschool classes to offer for next year's enrollment. Each toddler class has 8 students, and each preschool class has 12 students. The school has space for no more than 96 students total, and they have up to 10 rooms available for toddler and preschool classes.

Which system of inequalities can be used to determine the number of toddler classes, x, and number of preschool classes, y, the daycare center can offer?

Answer 1

First we define the variables:
 x = the number of toddler classes
 y = number of preschool classes
 We write then the system of inequations based on the following facts:
 "Each toddler class has 8 students, and each preschool class has 12 students." The school has space for no more than 96 students total "
 8x + 12y <= 96
 "they have up to 10 rooms available for toddler and preschool classes"

 x + y <= 10

 Answer:
 8x + 12y <= 96
 x + y <= 10
 option 1

Answer 2

Number of toddler classes: x
Number of preschool classes: y

Each toddler class has 8 students, and each preschool class has 12 students:
Total number of students: 8x+12y

The school has space for no more than 96 students total:
8x+12y<=96

They have up to 10 rooms available for toddler and preschool classes.
x+y<=10

Answer: First option
8x+12y<=96
x+y<=10