Respuesta :
Given:
Let x denotes the shirts, y denotes pairs of slacks and z denotes sports coat .
From the given information the three equations formed as,
[tex]\begin{gathered} 2x+2y=14.96\ldots\ldots..\ldots.\ldots(1) \\ 6x+3y+z=36.40\ldots\ldots\ldots(2) \\ 4x+z=15.95\ldots\ldots\ldots\ldots\text{.}(3) \end{gathered}[/tex]Solve the equations using substituion,
[tex]\begin{gathered} equation\text{ (1)} \\ 2x+2y=14.96 \\ x+y=7.48 \\ y=\text{7}.48-x\text{ Put it in equation (2)} \\ 6x+3(7.48-x)+z=36.40 \\ 6x+22.44-3x+z=36.40 \\ 3x+z=13.96\ldots\ldots\text{.}(4) \end{gathered}[/tex]Subtract equation 4 from 3,
[tex]\begin{gathered} 4x+z-(3x+z)=15.95-13.96 \\ 4x+z-3x-z=1.99 \\ x=1.99 \end{gathered}[/tex]Put the values in equation (1),
[tex]\begin{gathered} 2x+2y=14.96 \\ 2(1.99)+2y=14.96 \\ 2y=14.96-3.98 \\ y=\frac{10.98}{2} \\ y=5.49 \end{gathered}[/tex]Put the value of x in equation (3),
[tex]\begin{gathered} 4x+z=15.95 \\ 4(1.99)+z=15.95 \\ z=15.95-7.96 \\ z=7.99 \end{gathered}[/tex]Answer:
The charges for each shirts = $ 1.99, each pair of slacks = $ 5.49 and
each sport coat = $ 7.99.
