Question

Marie's room was covered with new wallpaper at a cost of $2 per square foot. Two walls measured 10 feet by 8 feet and the other two walls were 12 feet by 8 feet. What was the total cost of the wallpaper?

Answer 1

`$704`

Explanation:

`color(blue)("Preamble")`

First of all, this question does not represent real life. Most wall paper is patterned. So you have the issue of pattern matching. The consequence of which is that there is wastage.

On top of this any one role has a fixed length so this again would result in wastage. The last role may, or may not, have a lot of wastage.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Answering the question")`

Assumption - there is no pattern matching and no wastage.

Method:
Determine the total area
Multiply that area by the cost per unit area

`color(brown)("Determine total area")`

2 walls at 10 feet by 8 feet `->2(10xx8)ft^2=160ft^2`
2 walls at 12 feet by 8 feet `->2(12xx8)ft^2=ul(192ft^2larr" Add")`
`color(white)("ddddddddddddddddddddddddddddddddddd")color(green)(352ft^2)`

`color(brown)("Determine total cost")`

You can cancel or manipulate units of measurement the same way you can numbers. See what I mean below. The `ft^2` cancel out.

Cost for each `ft^2` is `$2 " per "ft^2` written as `color(red)(($2)/(ft^2))`

Total cost `color(red)(" cost for each square foot ")xxcolor(green)(" count of square feet")`
`color(white)("ddddddddddddddddd")color(red)(($2)/(cancel(ft^2)))color(white)("d.dddddd.")xxcolor(white)("dddddddd")color(green)(352cancel(ft^2))`

`$2xx352 = $704`