Respuesta :
Let Angie's share be
[tex]=x[/tex]Let Marie's share be
[tex]=y[/tex]Let Gwen's share be
[tex]=z[/tex]$125 is to be divided among three servers can be represented as
[tex]x+y+z=125\ldots\ldots\ldots(1)[/tex]Angie made $15 more than Marie can be represented as
[tex]x=y+15\ldots\ldots(2)[/tex]Gwen, who went home sick, made 28 less than Marie can be represented as
[tex]z=y-28\ldots\ldots\text{.}\mathrm{}(3)[/tex]Substitute equations (2) and (3) in equation (1)
[tex]\begin{gathered} x+y+z=125 \\ y+15+y+y-28=125 \\ \text{collect similar terms} \\ y+y+y+15-28=125 \\ 3y-13=128 \\ \text{add 13 to both sides} \\ 3y-13+13=125+13 \\ 3y=138 \\ \text{divide both sides by 3} \\ \frac{3y}{3}=\frac{138}{3} \\ y=46 \end{gathered}[/tex]Substitute y = 46 in equations (2) and (3)
[tex]\begin{gathered} x=y+15 \\ x=46+15 \\ x=61 \end{gathered}[/tex][tex]\begin{gathered} z=y-28 \\ z=46-28 \\ z=18 \end{gathered}[/tex]Therefore,
Angie's share = $61
Marie's share = $46
Gwen's share = $18
