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
Introduction
Determining the number of toddler and preschool classes to offer for next year's enrollment is a crucial decision for a daycare center. The school needs to ensure that it has enough space to accommodate the expected number of students while also providing a suitable learning environment. In this scenario, we are given that each toddler class has 8 students and each preschool class has 12 students. The school has space for no more than 120 students. We need to determine the number of toddler and preschool classes that the school can offer for next year's enrollment.
Calculating the Number of Classes
Let's assume that the school wants to offer x toddler classes and y preschool classes. Since each toddler class has 8 students, the total number of students in the toddler classes will be 8x. Similarly, since each preschool class has 12 students, the total number of students in the preschool classes will be 12y.
We know that the school has space for no more than 120 students. Therefore, the total number of students in the toddler and preschool classes should not exceed 120. We can write this as an inequality:
8x + 12y ≤ 120
Solving the Inequality
To solve the inequality, we can start by isolating one of the variables. Let's isolate x:
8x ≤ 120 - 12y x ≤ (120 - 12y) / 8
Since x must be a whole number (we can't have a fraction of a class), we can round down the right-hand side of the inequality to the nearest whole number.
x ≤ ⌊(120 - 12y) / 8⌋
Finding the Maximum Number of Toddler Classes
Now that we have the inequality, we can find the maximum number of toddler classes that the school can offer. To do this, we can try different values of y and see how many toddler classes we can fit.
Let's start with y = 0. In this case, the inequality becomes:
x ≤ (120 - 0) / 8 x ≤ 15
So, if the school offers no preschool classes, it can offer up to 15 toddler classes.
Finding the Maximum Number of Preschool Classes
Now that we have the inequality, we can find the maximum number of preschool classes that the school can offer. To do this, we can try different values of x and see how many preschool classes we can fit.
Let's start with x = 0. In this case, the inequality becomes:
12y ≤ 120 y ≤ 10
So, if the school offers no toddler classes, it can offer up to 10 preschool classes.
Finding the Optimal Solution
Now that we have the maximum number of toddler and preschool classes that the school can offer, we need to find the optimal solution. To do this, we can try different combinations of toddler and preschool classes and see which one maximizes the total number of students.
Let's start with x = 10 and y = 5. In this case, the total number of students is:
8x + 12y = 8(10) + 12(5) = 80 + 60 = 140
This is less than the maximum number of students that the school can accommodate, so we can try increasing the number of toddler classes.
Let's try x = 12 and y = 4. In this case, the total number of students is:
8x + 12y = 8(12) + 12(4) = 96 + 48 = 144
This is still less than the maximum number of students that the school can accommodate, so we can try increasing the number of toddler classes again.
Let's try x = 15 and y = 3. In this case, the total number of students is:
8x + 12y = 8(15) + 12(3) = 120 + 36 = 156
This is more than the maximum number of students that the school can accommodate, so we need to decrease the number of toddler classes.
Let's try x = 14 and y = 3. In this case, the total number of students is:
8x + 12y = 8(14) + 12(3) = 112 + 36 = 148
This is still more than the maximum number of students that the school can accommodate, so we need to decrease the number of toddler classes again.
Let's try x = 13 and y = 3. In this case, the total number of students is:
8x + 12y = 8(13) + 12(3) = 104 + 36 = 140
This is equal to the maximum number of students that the school can accommodate, so we have found the optimal solution.
Conclusion
In this scenario, the daycare center can offer up to 13 toddler classes and 3 preschool classes for next year's enrollment. This will allow the school to accommodate a total of 140 students, which is the maximum number of students that the school can accommodate.
Optimal Solution Summary
| Class Type | Number of Classes | Total Number of Students |
|---|---|---|
| Toddler | 13 | 104 |
| Preschool | 3 | 36 |
| Total | 16 | 140 |
Introduction
In our previous article, we discussed how to determine the number of toddler and preschool classes to offer for next year's enrollment. We used an inequality to find the maximum number of classes that the school can offer, and we found that the optimal solution is to offer 13 toddler classes and 3 preschool classes. In this article, we will answer some frequently asked questions about this scenario.
Q: What is the maximum number of students that the school can accommodate?
A: The maximum number of students that the school can accommodate is 120.
Q: How many toddler classes can the school offer if it offers no preschool classes?
A: If the school offers no preschool classes, it can offer up to 15 toddler classes.
Q: How many preschool classes can the school offer if it offers no toddler classes?
A: If the school offers no toddler classes, it can offer up to 10 preschool classes.
Q: What is the optimal solution for the number of toddler and preschool classes to offer?
A: The optimal solution is to offer 13 toddler classes and 3 preschool classes.
Q: What is the total number of students that the school can accommodate with the optimal solution?
A: The total number of students that the school can accommodate with the optimal solution is 140.
Q: How can the school determine the number of classes to offer for next year's enrollment?
A: The school can use the inequality 8x + 12y ≤ 120 to determine the number of classes to offer. This inequality represents the maximum number of students that the school can accommodate.
Q: What are the benefits of offering 13 toddler classes and 3 preschool classes?
A: The benefits of offering 13 toddler classes and 3 preschool classes include:
- Providing a suitable learning environment for 140 students
- Meeting the maximum number of students that the school can accommodate
- Offering a variety of classes to cater to different learning styles and needs
Q: What are the challenges of determining the number of classes to offer for next year's enrollment?
A: The challenges of determining the number of classes to offer for next year's enrollment include:
- Ensuring that the school has enough space to accommodate the expected number of students
- Providing a suitable learning environment for all students
- Meeting the needs of different learning styles and abilities
Conclusion
In this article, we have answered some frequently asked questions about determining the number of toddler and preschool classes to offer for next year's enrollment. We have discussed the optimal solution, the benefits and challenges of offering 13 toddler classes and 3 preschool classes, and how the school can use the inequality 8x + 12y ≤ 120 to determine the number of classes to offer.
Optimal Solution Summary
| Class Type | Number of Classes | Total Number of Students |
|---|---|---|
| Toddler | 13 | 104 |
| Preschool | 3 | 36 |
| Total | 16 | 140 |
Note: The total number of students is the sum of the number of students in the toddler and preschool classes.