Math Help for Section 3.3, Page 123

Markups
and Discounts
The
mathematics of discounts is similar to that of markups, but discount is
taken off the original selling price, whereas markup is added to the
cost. 

If you solve the sale price model for discount, you get the
following equivalent model.

If you substitute the model

into the model

    , 

you get the following model for sale price, in terms of
original price and discount rate.

Example
7: Check

$\eqalign{\textbf{a.}\quad 60 =& p\left( {199.95}
\right)&{\small\color{red}\quad\quad\text{Write original equation.}} \cr 60 \overset{?}{=}& \left( {\color{red}0.30}
\right)\left( {199.95}
\right)&{\small\color{red}\quad\quad\text{Substitute 0.30 for }p.} \cr 60 \approx&
59.985&{\small\color{red}\quad\quad\text{Solution checks. }
\checkmark}
\cr} $

$\eqalign{\textbf{b.}\quad\quad x =& 3.49 – \left( {0.4}
\right)\left(
{3.49} \right)&{\small\color{red}\quad\quad\text{Write
original equation.}} \cr
\color{red}2.09\color{black}\overset{?}{=}& 3.49 –
\left( {0.4} \right)\left( {3.49}
\right)&{\small\color{red}\quad\quad\text{Substitute 2.09
for }x.} \cr 2.09\overset{?}{=}& 3.49 –
1.396&{\small\color{red}\quad\quad\text{Multiply.}} \cr 2.09
\approx&
2.094&{\small\color{red}\quad\quad\text{Solution checks. }\checkmark}\cr} $

Recall that the symbol $ \approx $ means “is approximately
equal to.”