Louis has three more quarters than dimes in his pocket, for a total of $1.80....

Write an equation to represent the number of dimes:
Let number of dimes be x and quarter be q.
Given that the value of quarters and dimes is $1.80
Given that Louis has three more quarters than dimes.
Thus, $q=x+3$.
$1$dime $=\$0.10$ and $1$ quarter $=\$0.25$.
$0.10x+0.25q=1.80$.
Substitute the value of q in above equation:
$$\begin{gathered} 0.10x+0.25(x+3)=1.80 \\ 0.10x+0.25x+0.75=1.80 \\ 0.35x+0.75=1.80 \end{gathered}$$
Hence, $0.35x+0.75=1.80$ is the required equation to represent the number of dimes, x in his pocket.