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Part 1

Let the supply and demand for bananas in cents per pound be given by the equations below.

​supply:

p =3/5 q ​demand: p equals 100 -2/5q

​(a)**** Graph these equations on the same axes.

​(b) Find the equilibrium quantity.

​(c)**** Find the equilibrium price.

​(d)**** At a price of 47 cents per​ pound, is there a surplus or a shortage of​ supply?

### Part 1: Supply and Demand for Bananas

We are given the supply and demand equations for bananas, where:

- **Supply equation**: \( p = \frac{3}{5}q \)
- **Demand equation**: \( p = 100 - \frac{2}{5}q \)

Where:
- \( p \) represents the price in cents per pound,
- \( q \) represents the quantity in pounds.

### (a) Graph these equations on the same axes

We need to graph both the supply and demand equations on the same set of axes, where the horizontal axis (x-axis) represents quantity (\( q \)) and the vertical axis (y-axis) represents price (\( p \)).

- **Supply curve**: The equation \( p = \frac{3}{5}q \) is a straight line that starts from the origin and has a positive slope.
  
- **Demand curve**: The equation \( p = 100 - \frac{2}{5}q \) is a straight line that starts from \( p = 100 \) on the y-axis and has a negative slope.

### (b) Find the equilibrium quantity

At equilibrium, the supply equals the demand. This means that the price (\( p \)) from the supply equation equals the price from the demand equation.

\[
\frac{3}{5}q = 100 - \frac{2}{5}q
\]

Solve for \( q \):

\[
\frac{3}{5}q + \frac{2}{5}q = 100
\]

\[
\frac{5}{5}q = 100
\]

\[
q = 100
\]

Thus, the equilibrium quantity is \( q = 100 \) pounds.

### (c) Find the equilibrium price

Now that we have the equilibrium quantity, we can substitute \( q = 100 \) into either the supply or demand equation to find the equilibrium price.

Using the supply equation:

\[
p = \frac{3}{5}(100) = 60 \, \text{cents}
\]

Thus, the equilibrium price is \( p = 60 \) cents per pound.

### (d) At a price of 47 cents per pound, is there a surplus or a shortage of supply?

To determine whether there is a surplus or shortage at \( p = 47 \) cents per pound, we need to find both the quantity supplied and the quantity demanded at this price.

#### Step 1: Find the quantity supplied at \( p = 47 \):

From the supply equation \( p = \frac{3}{5}q \):

\[
47 = \frac{3}{5}q
\]

Solving for \( q \):

\[
q = \frac{47 \times 5}{3} = 78.33 \, \text{pounds}
\]

#### Step 2: Find the quantity demanded at \( p = 47 \):

From the demand equation \( p = 100 - \frac{2}{5}q \):

\[
47 = 100 - \frac{2}{5}q
\]

Solving for \( q \):

\[
\frac{2}{5}q = 100 - 47 = 53
\]

\[
q = \frac{53 \times 5}{2} = 132.5 \, \text{pounds}
\]

#### Step 3: Conclusion

At \( p = 47 \) cents per pound:
- Quantity supplied: \( 78.33 \, \text{pounds} \)
- Quantity demanded: \( 132.5 \, \text{pounds} \)

Since the quantity demanded is greater than the quantity supplied, there is a **shortage** of supply.

---

Do you want me to graph the equations for part (a)? Let me know if you'd like more details on any part.

### 5 Related Questions:
1. How does the slope of the supply and demand curves affect equilibrium?
2. What happens to equilibrium if the supply or demand curves shift?
3. How do taxes or subsidies impact the equilibrium price and quantity?
4. Can you explain the concept of price elasticity of demand and supply?
5. What is the difference between a surplus and a shortage?

**Tip**: The equilibrium point is where the quantity supplied equals the quantity demanded, ensuring no surplus or shortage occurs.

Let the supply and demand for bananas in cents per pound be given by the equations below.

supply: p = 3/5 q 
demand: p = 100 - 2/5 q 

(a) Graph these equations on the same axes.
(b) Find the equilibrium quantity.
(c) Find the equilibrium price.
(d) At a price of 47 cents per pound, is there a surplus or a shortage of supply?

Learn how to graph the supply and demand equations for bananas, find the equilibrium quantity and price, and determine if there's a surplus or shortage at a given price. This detailed explanation covers linear equations and equilibrium concepts, suitable for Grades 9-12.

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