Question

You invest $15,000 to start a hot dog stand at the local sports complex. It costs you $.65 to produce each hot dog. How many hot dogs must you sell before your average cost per hot dog is $1.15?
The answer should be 30,000. I just do not understand how to get to it.

Thank you in advance!

Answer 1

Answer:

• Below is the procedure to find the answer: 30,000 hot dogs.

Explanation:

The average cost is found dividing the total cost by the number of hot dogs:

         $Average\text{ }cost=Total\text{ }cost/Number\text{ }of\text{ }hot\text{ }dogs$

The total cost is the the sum of amount that you invest plus the product of the cost of producing each hot dog times the number of hot dogs:

$Total\text{ }cost=investment+Number\text{ }of\text{ }hot\text{ }dogs\times cost\text{ }to\text{ }produce\text{ }each\text{ }hot\text{ }dog$

• Substitute the values:

           $Total\text{ }cost=15,000+0.65x\\ \\ Averate\text{ }cost=(15,000+0.65x)/x=1.15$

Where x is the number of hot dogs.

• Solve for x from the equation:

         $(15,000+0.65x)/x=1.15\\ \\ 15,000+0.65x=1.15x\\ \\ 15,000=1.15x-0.65x\\ \\ 15,000=0.5x\\ \\ 15,000/0.5=x\\ \\ 30,000=x\\ \\ x=30,000$

Which shows you how you can find that the answer is 30,000 hot dogs.