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}$