Question

what is the cost of painting the walls and ceiling of a room with walls 30 foot by 25 foot by 1st foot with paint that covers at $9.50 per square yard, allowing for 1275 square feet for doors, windows, and baseboards?

Answer 1

What I can make out is, check the picture, that'd be the dimensions of the room.

therefore, the surface area of that room is

2 10x25 rectangles, front and back

2 30x10 rectangles, left and right

and 2 25x30 rectangles, top and bottom

so the area will be (2*10*25) + (2*30*10) + (2*25*30), which gives us  2600 square feet though, not yards.

let's add the doors, windows and others which is 1275, so 2600 + 1275, that gives us 3875 square feet.

now, the paint is 9.5 for square yard, no feet, so let's do some conversion then,

$\bf \begin{array}{ll} yards&feet\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 1yd&3ft\\ (1yd)^2&(3ft)^2\\ yd^2&3^2ft^2\\ &9ft^2 \end{array}$

so, if there are 9 square feet in one square yard, how many square yards are there in 3875 square feet?

$\bf \begin{array}{ccll} yd^2&ft^2\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 1&9\\ x&3875 \end{array}\implies \cfrac{1}{x}=\cfrac{9}{3875}\implies \cfrac{3875}{9}=x$

that's how many yd² are there in 3875 ft².

now, we know for every yd², is $9.50, so then the cost will be 

$\bf 9.5\cdot \cfrac{3875}{9}\implies \cfrac{95}{10}\cdot \cfrac{3875}{9}\implies \cfrac{73625}{18}~~\approx~~ \stackrel{\ }{4090.2778}$