It costs $ 500 to start up a business of selling hot dogs. Each hot dog costs $ 0.75 to produce. Let y be the cost in dollars of producing x hot dogs. How many hot dogs will be produced if total cost is $ 1 comma 775​?

Question

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Part 1
A.
17 hot dogs
B.
170 hot dogs
C.
1 comma 700 hot dogs
D.
3 comma 400 hot dogs

Answer 1

To find out how many hot dogs can be produced for a total cost of $1,775, we first need to understand the total cost equation, which consists of the startup cost and the production cost.

The total cost \( y \) can be represented as:

\[ y = \text{startup cost} + \text{production cost} \]

In this case:

• The startup cost is $500.
• The production cost for \( x \) hot dogs is \( 0.75x \).

So, the equation becomes:

\[ y = 500 + 0.75x \]

We need to find \( x \) when the total cost \( y \) is $1,775. Therefore, we set up the equation:

\[ 1775 = 500 + 0.75x \]

Now, we can solve for \( x \):

1. Subtract 500 from both sides:

\[ 1775 - 500 = 0.75x \]

\[ 1275 = 0.75x \]

2. Now, divide both sides by 0.75:

\[ x = \frac{1275}{0.75} \]

3. Calculate \( x \):

\[ x = 1700 \]

Thus, the number of hot dogs that can be produced for a total cost of $1,775 is 1,700 hot dogs.

So the correct answer is C. 1,700 hot dogs.