Question

type the correct answer in each box. use numerals instead of words. if necessary, use / for the fraction bar(s)
john hosts an art workshop on the weekends. he has an average of 14 students in each session and charges a fee of $12 per session. he estimates that for every $2 increase in the fee, the average number of students reduces by 1.
complete the equation that models this scenario, where c(x) is the revenue generated and x is the number of $2 fee increases.
$c(x) = square x^2 + square x + square$

Explanation:

Step1: Define fee per student

Fee per student: $12 + 2x$

Step2: Define number of students

Number of students: $14 - x$

Step3: Expand revenue formula

Revenue $c(x) = (12+2x)(14-x)$
$= 12*14 -12x +28x -2x^2$
$= 168 +16x -2x^2$

Step4: Rearrange to standard form

$c(x) = -2x^2 +16x +168$

Answer:

$c(x) = \boldsymbol{-2}x^2 + \boldsymbol{16}x + \boldsymbol{168}$