Question

select the correct answer.
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?
a. ( 8x + 12y geq 10 )
( x + y < 96 )
b. ( 8x + 12y leq 10 )
( x + y leq 96 )
c. ( 8x + 12y < 96 )
( x + y > 10 )
d. ( 8x + 12y leq 96 )
( x + y leq 10 )

Explanation:

Step1: Define total student constraint

Each toddler class has 8 students ($x$ classes) and each preschool class has 12 students ($y$ classes). Total students cannot exceed 96, so:
$8x + 12y \leq 96$

Step2: Define total room constraint

Total number of classes (rooms) cannot exceed 10, so:
$x + y \leq 10$

Step3: Match to options

The two inequalities match option D.

Answer:

D. $8x + 12y \leq 96$
$x + y \leq 10$