Math Help for Section 3.5, Page 138

Solving
Mixture Problems
Mixture problems are usually composed of the sum of two or more “hidden
products” that involve rate
factors. Here is the generic form of the verbal model for
mixture problems. Each compound in the model is a product of a rate
factor (labeled First rate and Second rate) and an amount.

    The rate factors are usually
expressed as percents
or percents of measure
such as dollars per pound,
jobs per hour, or gallons per minute.

Example
3: Check

    $\eqalign{0.045x + 0.055(10,000 – x)
=&
508.75&{\small\color{red}\quad\quad\text{Write original
equation.}} \cr 0.045\left( {\color{red} 4125} \right) + 0.055\left(
10,000-{\color{red} 4125} \right) \overset{?}{=}&
508.75&{\small\color{red}\quad\quad\text{Substitute 4125
for } x.} \cr 185.625 + 323.125 \overset{?}{=}&
508.75&{\small\color{red}\quad\quad\text{Subtract and
multiply.}} \cr 508.75 =&
508.75&{\small\color{red}\quad\quad\text{Solution checks. }\checkmark} \cr} $