 solve it in rational function form like R(x)= p(x)/q(x)

Certainly! Let's solve the third problem using a rational function.

### **Problem: Demand and Supply of Agricultural Products**
- **Demand for bananas:** \( D = 2000 \) pieces
- **Supply of bananas:** \( S = 1500 \) pieces

We want to find out how many more bananas are needed to meet the demand using a rational function of the form \( R(x) = \frac{p(x)}{q(x)} \).

### **Rational Function Formulation**

Let's define the rational function \( R(x) \) that represents the difference between demand and supply:

\[
R(x) = \frac{D(x) - S(x)}{1}
\]

Here:
- \( p(x) = D(x) - S(x) \) (the difference between demand and supply)
- \( q(x) = 1 \) (since we want the output directly without scaling or transforming it)

Substituting the given values:

\[
R(x) = \frac{2000 - 1500}{1}
\]

Simplifying the expression:

\[
R(x) = \frac{500}{1} = 500
\]

So, the rational function \( R(x) = \frac{500}{1} \) represents the additional number of bananas needed to meet the demand.

### **Interpretation**
The rational function \( R(x) \) tells us that **500 more bananas** are needed to meet the demand.

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Would you like more details on this approach or have any questions?

Here are 5 related questions you might explore:

1. How would \( R(x) \) change if the supply of bananas was a function of time, such as \( S(x) = 1000 + 100x \)?
2. If the demand \( D(x) \) also varied with time, how would you express the difference in terms of \( R(x) \)?
3. Can you express the relationship between demand and supply if both \( D(x) \) and \( S(x) \) were quadratic functions?
4. What happens to \( R(x) \) if the demand increases by 50% while the supply remains constant?
5. How can rational functions be used to model more complex supply and demand scenarios, such as when multiple products are involved?

**Tip:** Rational functions are highly versatile and can model various scenarios where relationships involve ratios or differences between quantities, such as rates of change or proportional relationships.

Learn how to solve the demand and supply problem of agricultural products using rational functions. This problem involves finding additional bananas needed to meet demand based on given supply data. Suitable for students in Grades 10-12.

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