Avery is in the business of manufacturing phones. She must pay a daily fixed cost to rent the building and equipment, and also pays a cost per phone produced for materials and labor. The labor and materials cost $100 for each phone manufactured, and the total cost of producing 3 phones in a day would be $600. Write an equation for C, commaC, in terms of p, commap, representing total cost, in dollars, of producing pp phones in a given day.

Question

Avery is in the business of manufacturing phones. She must pay a daily fixed cost to rent the building and equipment, and also pays a cost per phone produced for materials and labor. The labor and materials cost $100 for each phone manufactured, and the total cost of producing 3 phones in a day would be $600. Write an equation for C, commaC, in terms of p, commap, representing total cost, in dollars, of producing pp phones in a given day.

Answer 1

Let C be the total cost of producing p phones in a day.

Since each phone costs $100 in labor and materials, the cost of p phones would be 100p dollars.

The fixed cost for renting the building and equipment is not dependent on the number of phones produced, so it can be represented as a constant value.

Given that the total cost of producing 3 phones in a day is $600, the equation for C in terms of p is:

C = 100p + C_fixed
600 = 100(3) + C_fixed
600 = 300 + C_fixed

Simplifying the equation, we find that C_fixed, the daily fixed cost, is:

C_fixed = 600 - 300
C_fixed = 300

So, the equation for C in terms of p is:

C = 100p + 300