Question

A contractor is hired to build an apartment complex. Each 840-square-foot unit has a bedroom, kitchen, and bathroom. The bedroom will be the same size as the kitchen. The owner orders 980 square feet of tile to completely cover the floors of two kitchens and two bathrooms. Determine how many square feet of carpet is needed for each bedroom.

Answer 1

350 sq ft

Explanation:

Given that:

840 sq ft area has a bedroom, kitchen and bathroom.

Let the area of bedroom be
`x` sq ft.

Then the area of kitchen will also be
`x` sq ft.

Let the area of bathroom be
`y` sq ft.

As per question statement:

`x+y+x=840\\\Rightarrow 2x+y=840 ...... (1)`

Tiles ordered to cover two kitchens and two bathrooms is 980 sq ft.

i.e.

`2x+2y=980 ..... (2)`

Subtracting equation (1) from (2):

i.e. (2) - (1):

`y = 140` sq ft

Putting the value of
`y` in (1):

`2x+140=840\\\Rightarrow 2x =700\\\Rightarrow \bold{x=350\ sq\ ft}`

Therefore, the carpet needed for each bedroom = 350 sq ft