Question

christine is a software salesperson. her base salary is $2100 and she makes $50 more for every copy of english is fun she sells. her total pay, p (in dollars), after selling c copies is given by the following function.\\( p(c) = 2100 + 50c \\)\
answer the following questions.\
(a) what is christine’s total pay if she sells 21 copies?\
$\square$\
(b) if christine’s total pay is $3800, how many copies did she sell?\
$\square$ copies

Explanation:

Part (a)

Step1: Identify the function and input

We have the total pay function \( P(c) = 2100 + 50c \), and we need to find \( P(21) \) (since \( c = 21 \) copies sold).

Step2: Substitute \( c = 21 \) into the function

Substitute \( c = 21 \) into \( P(c) \):
\( P(21)=2100 + 50\times21 \)
First, calculate \( 50\times21 = 1050 \).
Then, \( 2100+1050 = 3150 \).

Part (b)

Step1: Set up the equation

We know \( P(c)=3800 \), so substitute into \( P(c) = 2100 + 50c \):
\( 3800 = 2100 + 50c \)

Step2: Solve for \( c \)

Subtract 2100 from both sides:
\( 3800 - 2100 = 50c \)
\( 1700 = 50c \)
Divide both sides by 50:
\( c=\frac{1700}{50}=34 \)

Answer:

(a) \(\$3150\)
(b) \(34\) copies