Question

Suppose carpet for a 12ft by 14ft room costs $400 find the cost to carpet a room 48ft by 56ft

Answer 1

`\$\ 6400`

Explanation:

1. Approach

The easiest way to solve this problem is to find the area of the first room with the dimensions of (12ft) by (14ft). Then one will divide the cost of carpeting the room by the area of the room, this will yield the price of carpeting per square foot. After finding the price of carpeting per square foot, one will find the area of the second room, with the dimensions of (48ft) by (56ft). Finally, one will multiply the price per square foot of carpeting by the area of the second room to find the price for carpeting the second room.

2. Find the area of the first room

Assume that the first room is a rectangle. the following formula can be used to find the area of a rectangle,

`(length)(width)=Area`

The following are the dimensions of the given room,

`length = 14\\width = 12`

Substitute into the formula to find the area and simplify to solve,

`(length)(width)=Area`

`(14)(12)=Area_1`

`168=Area_1`

3. Find the price of carpeting per square foot

To find the price of carpeting per square foot, divide the total price for carpeting the first room by the area of the first room.

`(carpeting\ price_1)/(area_1)`

`=(400)/(168)`

Simplify,

`=(400)/(168)`

`=(50)/(21)`

4. FInd the area of the second room

Assume that the second room is also a rectangle. Use a similar strategy to find the area of this room as used for the area of the first room.

`(length)(width)=Area`

`length = 48\\width = 56`

Substitute and simplify to sovle,

`(length)(width)=Area`

`(48)(56)=Area_2`

`2688=Area_2`

5. Find the price for carpeting the room

Multiply the area of the room by the price for carpeting per square foot to find the price for carpeting the second room.

`(Area_2)*(carpeting\ price)`

`2688=Area_2`

`(50)/(21)=carpeting\ price`

`(Area_2)*(carpeting\ price)`

`=(2688)*((50)/(21))`

Simplify to solve,

`=(2688)*((50)/(21))`

`=(2688)*((50)/(21))`

`=6400`