Question

Carolina makes hand towels which cost $2 each to make, but she charges a $50 start-up fee for every job she does. Write an equation representing the total cost to make towels.

A) C(x) = 2x
B) C(x) = 50 + 2x
C) C(x) = 2x - 50
D) C(x) = 50x + 2

Answer 1

The correct equation representing the total cost to make towels, including a $50 start-up fee and a $2 production cost per towel, is C(x) = 50 + 2x.

Step-by-step explanation:

The equation that represents the total cost to make towels, taking into consideration both the $50 start-up fee and the $2 production cost per towel, would be C(x) = 50 + 2x. Here, x represents the number of towels Carolina makes. This equation is a linear equation where the $50 is a fixed cost (the y-intercept), and the $2 is the variable cost per towel (the slope).

Using similar examples, such as a specialty cleaning company with a session fee and hourly rate or a tutor that charges a one-time fee and per hour, we see the same structure in their cost equations. These examples all reflect a common form where the total cost equals a fixed fee plus a variable fee multiplied by the quantity.