Question

you bought some tile that cost four dollars per square foot and some carpet that cost two dollars per square foot. A total of 2500 ft.² was purchased for $6800 your friend thought that you purchased 1600 ft.² of tile, and 900 feet of carpet. Decide if your friend is correct, if your friend is correct, explain why. If your friend is not correct, explain the error in their reasoning.

Answer 1

`\begin{gathered} \text{The tile cost \$4 per square foot} \\ \text{The carpet cost \$2 per square foot} \end{gathered}`

let

x = square ft of tile bought

y = square ft of carpet bought

Therefore,

`\begin{gathered} x+y=2500\ldots\ldots\ldots\ldots......(1) \\ 4x+2y=6800\ldots\ldots\ldots\ldots\ldots\text{.(2)} \\ x=2500-y \\ 2x+y=3400 \\ 2(2500-y)+y=3400 \\ 5000-2y+y=3400 \\ 3400-5000=-y \\ -1600=-y \\ y=1600ft^2 \\ x+1600=2500 \\ x=2500-1600 \\ x=900ft^2 \end{gathered}`

Your friend is incorrect because he said the tile he purchased is 1600 ft square but base on the equation formed the tile should be 900 ft squared and the carpet should be 1600 square ft. The error their was that he interchanged the square feet value of the carpet and the tiles.