College Algebra 9th txtbk

SECTION 2–4 Linear Equations and Models 149
MATCHED PROBLEM 1
The following linear equation expresses BSA for felines in terms of weight:
a 28.55w 118.7
where a is BSA in square inches and w is weight in pounds.
(A) Interpret the slope of the BSA equation.
(B) What is the effect of a 1-pound increase in weight?
Z Linear Models
We can use our experience with lines in Section 2-3 to construct linear models for applications
involving linearly related quantities. This process is best illustrated through examples.
EXAMPLE 2
Business Markup Policy
A sporting goods store sells a fishing rod that cost $60 for $82 and a pair of cross-country
ski boots that cost $80 for $106.
(A) If the markup policy of the store for items that cost more than $30 is assumed to be
linear, find a linear model that express the retail price P in terms of the wholesale
cost C.
(B) What is the effect on the price of a $1 increase in cost for any item costing over $30?
(C) Use the model to find the retail price for a pair of running shoes that cost $40.
SOLUTIONS
(A) If price P is linearly related to cost C, then we are looking for the equation of a line
whose graph passes through (C 1 , P 1 ) (60, 82) and (C 2 , P 2 ) (80, 106). We find
the slope, and then use the point–slope form to find the equation.
m P 2 P 1 106 82
C 2 C 1 80 60 24
20 1.2 Substitute C 1 60, P 1 82, C 2 80,
and P 2 106 into the slope formula.
P P 1 m(C C 1 )
P 82 1.2(C 60)
P 82 1.2C 72
P 1.2C 10 C 7 30
Substitute P 1 82, C 1 60, and
m 1.2 into the point–slope formula.
Distribute
Add 82 to both sides.
Linear model
(B) If the cost is increased by $1, then the price will increase by 1.2(1) $1.20.
(C) P 1.2(40) 10 $58.
MATCHED PROBLEM 2 The sporting goods store in Example 2 is celebrating its twentieth anniversary with a 20%
off sale. The sale price of a mountain bike is $380. What was the presale price of the bike?
How much did the bike cost the store?
ZZZ EXPLORE-DISCUSS 1
The wholesale supplier for the sporting goods store in Example 2 offers the store a
15% discount on all items. The store decides to pass on the savings from this discount
to the consumer. Which of the following markup policies is better for the consumer?
1. Apply the store’s markup policy to the discounted cost.
2. Apply the store’s markup policy to the original cost and then reduce this price
by 15%.
Support your choice with examples.