A custom t-shirt printing company charges a one-time design setup fee plus a fixed price f… — SAT

A custom t-shirt printing company charges a one-time design setup fee plus a fixed price for each t-shirt printed. The total cost, $C$ , in dollars, for an order of $n$ t-shirts is given by the equation $C = 15n + 50$ . What does the number $50$ represent in this equation?

The one-time design setup fee, in dollarsAnswer
B
The price, in dollars, for each printed t-shirt
C
The total cost, in dollars, for an order of 1 t-shirt
D
The number of t-shirts that are printed in an order that has no setup fee

Answer

The one-time design setup fee, in dollars

The constant term

50

in the linear equation

C = 15n + 50

represents the initial value of the cost function when no t-shirts are ordered (

n = 0

). In this context, this represents the one-time design setup fee.

Step-by-Step Solution

Identify the structure of the linear equation

C = 15n + 50

The equation is in the slope-intercept form

y = mx + b

, where

C

is the total cost,

n

is the number of t-shirts,

15

is the slope, and

50

is the y-intercept.

Analyzing the linear equation structure helps map its parts to the contextual scenario.

Interpret the constant term

50

within the context.

The constant term represents the value of

C

when

n = 0

, which is

C = 15(0) + 50 = 50

dollars.

When no t-shirts are printed, the only cost incurred is the initial flat setup fee.

Key Concept

Interpreting the y-intercept of a linear relationship in context

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

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