College Algebra 9th txtbk

142 CHAPTER 2 GRAPHS
MATCHED PROBLEM 7
Given the line L: 4x 2y = 3 and the point P = (2, 3), find an equation of a line through
P that is
(A) Parallel to L
(B) Perpendicular to L
Write the final answers in the slope–intercept form y = mx b.
EXAMPLE 8 Cost Analysis
A hot dog vendor pays $25 per day to rent
a pushcart and $1.25 for the ingredients in
one hot dog.
(A) Find the cost of selling x hot dogs in
1 day.
(B) What is the cost of selling 200 hot
dogs in 1 day?
(C) If the daily cost is $355, how many hot
dogs were sold that day?
SOLUTIONS
(A) The rental charge of $25 is the vendor’s fixed cost—a cost that is accrued every day
and does not depend on the number of hot dogs sold. The cost of the ingredients for
x hot dogs is $1.25x. This is the vendor’s variable cost—a cost that depends on the
number of hot dogs sold. The total cost for selling x hot dogs is
C(x) 1.25x 25
Total Cost Variable Cost Fixed Cost
(B) The cost of selling 200 hot dogs in 1 day is
C(200) 1.25(200) 25 $275
(C) The number of hot dogs that can be sold for $355 is the solution of the equation
1.25x 25 355
1.25x 330
x 330
1.25
264 hot dogs
Subtract 25 from each side.
Divide both sides by 1.25.
Simplify.
MATCHED PROBLEM 8
It costs a pretzel vendor $20 per day to rent a cart and $0.75 for each pretzel.
(A) Find the cost of selling x pretzels in 1 day.
(B) What is the cost of selling 150 pretzels in 1 day?
(C) If the daily cost is $275, how many pretzels were sold that day?