We have the following:
let x number of dimes
let y number of quarters
[tex]\begin{gathered} 0.10x+0.25y\ge3.6 \\ x+y\ge18 \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} x=12 \\ 12+y\ge18 \\ y\ge18-12 \\ y\ge6 \\ 0.10\cdot12+0.25y\ge3.6 \\ 1.2+0.25y\ge3.6 \\ y\ge\frac{3.6-0.12}{0.25} \\ y\ge9.6 \end{gathered}[/tex]Therefore, The quarters can range from 6 coins to 9.6 coins, that is, the maximum can be 10 coins.
