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, in terms of p, representing total cost, in dollars, of producing p phones in a
given day.
Answer: C=?

Answer 1

The equation that represents the total cost in dollars is C = 100p + 300

Explanation:

The form of the linear equation is y = m x + b, where

• m is the slope ⇒ rate of change

• b is the y-intercept ⇒ fixed amount

∵ Avery must pay a daily fixed cost to rent the building and equipment

∴ There is a fixed amount b

∵ She pays a cost per phone produced for materials and labor

∴ There is a rate m

∵ C represents the total cost of producing p phones in dollars

→ Form the linear equation for the situation

∴ The equation is C = m p + b

∵ The labor and materials cost $100 for each phone

∴ m = 100

→ Substitute it in the equation above

∴ C = 100p + b

∵ The cost of producing 3 phones in a day would be $600

∴ p = 3 and C = 600

→ Substitute them in the equation above to find b

∵ 600 = 100(3) + b

∴ 600 = 300 + b

→ Subtract 300 from both sides to find b

∵ 600 - 300 = 300 - 300 + b

∴ 300 = b

→ Substitute it in the equation

∴ C = 100p + 300

∴ The equation that represents the total cost in dollars is C = 100p + 300