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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 \\
x + y \leq 96[/tex]

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

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

D. [tex]\begin{aligned}
8x + 12y &\ \textless \ 96 \\
x + y &\ \textgreater \ 10
\end{aligned}[/tex]



Answer :

GinnyAnswer
To determine the number of toddler classes [tex]\( x \)[/tex] and preschool classes [tex]\( y \)[/tex] that the daycare center can offer, we need to establish a system of inequalities based on the given constraints:

1. Each toddler class has 8 students, and each preschool class has 12 students. The total number of students cannot exceed 96.
2. The daycare center has a maximum of 10 rooms for these classes.

We start by formulating the inequality based on the maximum number of students:

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

This inequality ensures that the total number of students in both toddler and preschool classes does not exceed 96.

Next, we formulate the inequality based on the number of rooms available:

[tex]\[ x + y \leq 10 \][/tex]

This inequality ensures that the total number of classes (both toddler and preschool) does not exceed the 10 available rooms.

Therefore, the correct system of inequalities is:

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

Reviewing the options, the answer is:

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