Question

$125 is to be divided among three servers. Angie made $15 more then Marie. Gwen, who went home sick, made 28 less then Marie. How much money should each server get?

Answer 1

Let Angie's share be

`=x`

Let Marie's share be

`=y`

Let Gwen's share be

`=z`

$125 is to be divided among three servers can be represented as

`x+y+z=125\ldots\ldots\ldots(1)`

Angie made $15 more than Marie can be represented as

`x=y+15\ldots\ldots(2)`

Gwen, who went home sick, made 28 less than Marie can be represented as

`z=y-28\ldots\ldots\text{.}\mathrm{}(3)`

Substitute equations (2) and (3) in equation (1)

`\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} \\ (3y)/(3)=(138)/(3) \\ y=46 \end{gathered}`

Substitute y = 46 in equations (2) and (3)

`\begin{gathered} x=y+15 \\ x=46+15 \\ x=61 \end{gathered}`
`\begin{gathered} z=y-28 \\ z=46-28 \\ z=18 \end{gathered}`

Therefore,

Angie's share = $61

Marie's share = $46

Gwen's share = $18