When the price of oranges is lowered by 40%, 4 more oranges can be purchased for $12 than can be puchased for the original price. How many oranges can be purchased for 24 dollars at the original price?

Options

A. 8
B. 12
C. 16
D. 20

Answer

To solve the problem step by step, we will follow the reasoning laid out in the video transcript.

### Step 1: Define Variables
Let:
- \( x \) = original price of one orange
- \( n \) = number of oranges that can be purchased for $12 at the original price.

### Step 2: Set Up the First Equation
From the information given, we know that the total cost for \( n \) oranges at the original price is:
\[ n \cdot x = 12 \]
This is our first equation.

### Step 3: Determine the New Price
When the price of oranges is lowered by 40%, the new price becomes:
\[ 0.6x \]

### Step 4: Set Up the Second Equation
According to the problem, after the price reduction, 4 more oranges can be purchased for the same $12. Therefore, the number of oranges that can be purchased at the new price is \( n + 4 \). The equation for this scenario is:
\[ (n + 4) \cdot (0.6x) = 12 \]

### Step 5: Simplify the Second Equation
Expanding the second equation gives:
\[ 0.6nx + 2.4x = 12 \]

### Step 6: Substitute the First Equation into the Second
From the first equation, we know that \( nx = 12 \). We can substitute \( nx \) in the second equation:
\[ 0.6(12) + 2.4x = 12 \]
This simplifies to:
\[ 7.2 + 2.4x = 12 \]

### Step 7: Solve for \( x \)
Now, isolate \( x \):
\[ 2.4x = 12 - 7.2 \]
\[ 2.4x = 4.8 \]
\[ x = \frac{4.8}{2.4} = 2 \]
Thus, the original price of one orange is $2.

### Step 8: Calculate the Number of Oranges for $24
To find out how many oranges can be purchased for $24 at the original price:
\[ \text{Number of oranges} = \frac{24}{x} = \frac{24}{2} = 12 \]

### Final Answer
The number of oranges that can be purchased for $24 at the original price is **12**.

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