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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, [tex]$x$[/tex], and number of preschool classes, [tex]$y$[/tex], the daycare center can offer?

A. [tex]$8x + 12y \leq 10$[/tex]
[tex][tex]$x + y \leq 96$[/tex][/tex]

B. [tex]$8x + 12y \geq 10$[/tex]
[tex]$x + y \ \textless \ 96$[/tex]

C. [tex][tex]$8x + 12y \ \textless \ 96$[/tex][/tex]
[tex]$x + y \ \textgreater \ 10$[/tex]

D. [tex]$8x + 12y \leq 96$[/tex]
[tex][tex]$x + y \leq 10$[/tex][/tex]



Answer :

GinnyAnswer
To determine the number of toddler classes ([tex]\(x\)[/tex]) and preschool classes ([tex]\(y\)[/tex]), we need to set up a system of inequalities that takes into account the constraints given in the problem:

1. Each toddler class has 8 students, and each preschool class has 12 students. The total number of students in all classes combined cannot exceed 96 students.
2. They can use up to 10 rooms for these classes.

We can express these constraints as inequalities:

- For the total number of students constraint: [tex]\(8x + 12y \leq 96\)[/tex]
- For the total number of rooms constraint: [tex]\(x + y \leq 10\)[/tex]

Therefore, the correct system of inequalities is:

[tex]\[ 8x + 12y \leq 96 \][/tex]
[tex]\[ x + y \leq 10 \][/tex]

So, the correct answer is:

D. [tex]\(8 x + 12 y \leq 96\)[/tex]
[tex]\[ x + y \leq 10 \][/tex]

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