Question

Alex took clothes to the cleaners three times last month. First, he brought 2 shirts and 2 pairs of slacks and paid $14.96. Then he brought 6 shirts, 3 pairs of slacks, and 1 sports coat and paid $36.40. Finally,he brought 4 shirts and 1 sports coat and paid $15.95 How much was he charged for each shirt each pair of stacks, and each sports coat?Alex was charged for each shirts for each pair of slacks, and for each sports coat

Answer 1

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,

`\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}`

Solve the equations using substituion,

`\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}`

Subtract equation 4 from 3,

`\begin{gathered} 4x+z-(3x+z)=15.95-13.96 \\ 4x+z-3x-z=1.99 \\ x=1.99 \end{gathered}`

Put the values in equation (1),

`\begin{gathered} 2x+2y=14.96 \\ 2(1.99)+2y=14.96 \\ 2y=14.96-3.98 \\ y=(10.98)/(2) \\ y=5.49 \end{gathered}`

Put the value of x in equation (3),

`\begin{gathered} 4x+z=15.95 \\ 4(1.99)+z=15.95 \\ z=15.95-7.96 \\ z=7.99 \end{gathered}`

Answer:

The charges for each shirts = $ 1.99, each pair of slacks = $ 5.49 and

each sport coat = $ 7.99.