A. The local barangay received a budget of ₱100, 000 to provide medical check-ups for the

children in the barangay. The amount is to be allotted equally among all the children in the

barangay. Write an equation representing the relationship of the allotted amount per child (y-

variable) versus the total number of children (x- variable).

Fill up the table with the different allotted amount for different number of children:

No. of children, x 10 20 50 100 200 300 500 1000

To determine the amount allotted per child (\( y \)) based on the total number of children (\( x \)), we start by understanding that the total budget of ₱100,000 is to be divided equally among all the children.

The equation representing this relationship is:
\[ y = \frac{100,000}{x} \]

Where:
- \( y \) is the allotted amount per child.
- \( x \) is the total number of children.

Now, let's fill in the table with the allotted amounts for the given numbers of children:

\[
\begin{array}{|c|c|}
\hline
\text{No. of children, } x & \text{Allotted amount per child, } y \\
\hline
10 & \frac{100,000}{10} = 10,000 \\
\hline
20 & \frac{100,000}{20} = 5,000 \\
\hline
50 & \frac{100,000}{50} = 2,000 \\
\hline
100 & \frac{100,000}{100} = 1,000 \\
\hline
200 & \frac{100,000}{200} = 500 \\
\hline
300 & \frac{100,000}{300} \approx 333.33 \\
\hline
500 & \frac{100,000}{500} = 200 \\
\hline
1000 & \frac{100,000}{1000} = 100 \\
\hline
\end{array}
\]

Thus, the completed table is:

| No. of children, \( x \) | Allotted amount per child, \( y \) |
|--------------------------|-----------------------------------|
| 10                       | 10,000                            |
| 20                       | 5,000                             |
| 50                       | 2,000                             |
| 100                      | 1,000                             |
| 200                      | 500                               |
| 300                      | 333.33                            |
| 500                      | 200                               |
| 1000                     | 100                               |

Would you like more details or have any questions?

Here are some related questions you might find interesting:
1. How would the equation change if the budget were increased to ₱200,000?
2. If the budget were to be shared equally among children and their parents, how would you modify the equation?
3. How many children can be provided medical check-ups if each check-up costs ₱250?
4. If 25% of the budget must be reserved for administrative costs, how does this affect the allotted amount per child?
5. What if the number of children were underestimated by 10%, how does this affect the budget allocation?
6. How would the equation change if each child were to receive a fixed amount of ₱500 instead?
7. If 150 more children move into the barangay, how does this affect the allotment per child?
8. How does the allotted amount per child change if the budget is only ₱80,000?

**Tip:** Understanding how to set up and manipulate equations to reflect real-world scenarios can help in budgeting and resource allocation.

Learn how to calculate the allotted amount per child with a ₱100,000 budget allocated equally among children in a barangay. Solve for different numbers of children and understand proportional reasoning. Suitable for students in Grades 4-6.

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