According to market research, the number of magzine subscriptions that can be sold can be estimated using this function
`n(p)=(5,000)/(4p-k)`, where n is the number of thousands of subscriptions sold, p is the price in dollars for each individual subscription, and k is some constant. If 250,000 subscriptions were sold at $15 for each subscription, how many subscriptions could be sold if the price were set at $20 for each subscription?

Options

A. `59,000`
B. `75,000`
C. `100,000`
D. `125,000`

Answer

To solve the problem step by step, we will follow the given function and the information provided.

### Step 1: Understand the function
The function given is:
\[ n(p) = \frac{5000}{4p - k} \]
where:
- \( n \) is the number of thousands of subscriptions sold,
- \( p \) is the price in dollars for each subscription,
- \( k \) is a constant.

### Step 2: Set up the equation with the known values
We know that 250,000 subscriptions were sold at $15 each. Since \( n \) is in thousands, we convert 250,000 to thousands:
\[ n = 250 \]
Now, substituting \( n \) and \( p \) into the function:
\[ 250 = \frac{5000}{4(15) - k} \]

### Step 3: Simplify the equation
Calculate \( 4(15) \):
\[ 4(15) = 60 \]
Now substitute this back into the equation:
\[ 250 = \frac{5000}{60 - k} \]

### Step 4: Solve for \( k \)
Cross-multiply to solve for \( k \):
\[ 250(60 - k) = 5000 \]
Expanding the left side:
\[ 15000 - 250k = 5000 \]
Now, isolate \( k \):
\[ 15000 - 5000 = 250k \]
\[ 10000 = 250k \]
Now divide both sides by 250:
\[ k = \frac{10000}{250} = 40 \]

### Step 5: Find the number of subscriptions sold at $20
Now we need to find out how many subscriptions could be sold if the price is set at $20. Substitute \( p = 20 \) and \( k = 40 \) back into the function:
\[ n(20) = \frac{5000}{4(20) - 40} \]

### Step 6: Simplify the new equation
Calculate \( 4(20) \):
\[ 4(20) = 80 \]
Now substitute this back into the equation:
\[ n(20) = \frac{5000}{80 - 40} \]
\[ n(20) = \frac{5000}{40} \]

### Step 7: Calculate \( n(20) \)
Now divide:
\[ n(20) = 125 \]
Since \( n \) is in thousands, the total number of subscriptions sold is:
\[ 125 \times 1000 = 125000 \]

### Conclusion
Thus, the number of subscriptions that could be sold at $20 each is **125,000**. Therefore, the correct option is **d) 125,000**.