[tex]\begin{gathered} \text{Let x be the number of half dollar she has, and y the number of quarters she has.} \\ \text{therefore we get the following equations} \\ 0.5x+0.25y=37.5 \\ 12y=x \\ \text{If we replace the second equation in the first one, we get} \\ 0.5\cdot12y+0.25y=37.5 \\ 6y+0.25y=37.5 \\ 6.25y=37.5 \\ y=\frac{37.5}{6.25}=6\text{ so she got 6 quarters} \\ \text{if y=6 we have that} \\ x=12\cdot y=12\cdot6=72\text{ halfs dollars} \end{gathered}[/tex]
