Answered

Get the answers you need at Westonci.ca, where our expert community is dedicated to providing you with accurate information. Discover in-depth answers to your questions from a wide network of experts on our user-friendly Q&A platform. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.

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, [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]

Sagot :

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]
We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.