College Algebra, Chapter 1, 1.2, Section 1.2, Problem 18

Express the value (in cents) of the change in a purse that contains twice as many nickels as pennies, four more dimes than nickels, and as many quarters as dimes and nickels combined. Suppose that $p$ = number of pennies.

Let $v$ be the value in cents of the change, so if we translate each statement in to algebra, we have

$
\begin{array}{|c|c|}
\hline\\
\text{In words} & \text{In Algebra} \\
\hline\\
\text{twice as many nickels as pennies} & n = 2p \\
\hline\\
\text{four more dimes them nickels} & d = 4 + n \\
\hline\\
\text{as many quarters as dimes and nickels combined} & q = d + n\\
\hline
\end{array}
$

Thus,


$
\begin{equation}
\begin{aligned}

v =& n + d + q
&&
\\
\\
v =& 2p + 4 + n + d + n
&& \text{Combine like terms}
\\
\\
v =& 2p + 2n + d + 4
&& \text{Make $n$ and $d$ in terms of $p$}
\\
\\
v =& 2p + 2(2p) + 4 + n + 4
&& \text{Simplify}
\\
\\
v =& 2p + 4p + n + 8
&& \text{Make $n$ in terms of $p$}
\\
\\
v =& 2p + 4p + (2p) + 8
&& \text{Combine like terms}
\\
\\
v =& 8p + 8
&&

\end{aligned}
\end{equation}
$