Consumer Math Question.(Home Renovation) 1 gallon paint can cover 500 feet^2?

[jolie]

Ok so I have this question.

So I am decorating a house on a home renovation question.

Heres the info:

A room has to be painted. The 4 walls and the ceiling. (not the floor)
The room is a rectangular prism with 1 door and 1 window.

The Ceiling is 8 ft tall. The width is 10 ft and the length is 12 ft

so wall 1 goes A = L * W
= 12*8 (ceiling)
= 96 ft^2

wall 2 goes A = L* W
= 12 * 8
= 96 ft^2

Wall 3 goes A = L*W
= 10 * 8
= 80 ft^2
Wall 4 goes A = L*W
= 10 * 8
= 80 ft^2

and the ceiling area goes A = L * W
= 12 * 10
= 120 ft^2

So the total are of the 4 walls and the Ceiling (not including the floor) is 472 ft^2

But the window and door can't be painted so you minus A = L* W
= 4* 3
= 12 ft^2 for the window
and A = L * W
= 2.5 * 6.5
= 16.25 FT^2

TOTAL AREA OF WINDOW AND DOOR = 28.25 ft^2

So 472 ft^2 minus 28.25^2 = 443.75 ft^2


So 443.72ft^2 has to be painted, that much we know.


The options for paint that I choose is 1 can of primer for $15 which covers 500 ft (only needs one coat)

and 2 cans of paint that covers 500 ft and costs $ 25 per can (the paint needs two coats)

A professional painter charges $35 an hour and can paint 250 ft^2 an hour.


MY QUESTION IS, HOW MUCH WILL ALL OF THIS COST?

I'm going to purchase 1 can of primer for $15 and 2 $25 pain cans which will come up to $65

The painter charges $35 an hour and works at 250ft^2 an hour so thats another $70 since the painter charges by the hour only. The area that needs to be painted is calculated at 443.75 ft^2

The painter can paint 500 ft^2 in two hours so that is $70 for the labour.

so Labour ($70) and paint/primer ($65) plus the service fee for supplies which comes upto ($50) all together = $185

But what I want to know is what is the mathematical procedure to figure exactly how much it would cost to paint an area of 443.75 ft^2 ?

Knowing that there will be some primer left and some paint especially.


500 ft - 443.75ft = 56.25ft so there will be 56.25ft of unused primer left in the can.

and the paint needs two coats so I will times 443.75 twice to get 887.50 ft

and times 500ft twice to get 1000 ft^2.

so 1000ft^2 - 887.5^2 = 112.5ft^2 of unusable paint left in the can.


Can someone double check my calculations for me ?

$15 divided by 500 = 0.03
0.03 times 443.75 = $ 13.31

$25 + $25 = $50
443.75 per coat times 2 = 887.5

$50 divided by 1000 = 0.05
0.05 times 887.5 = $ 44.38

$13.31 + $44.38 = $57.69

plus the $185 = $ 242.69

Does that sound right to anyone?

$242.69 all together? service fee, exact price per foot with the primer and paint?


Or do I take $15 - $13.31 = $1.69
and $ 50 - $44.38 = $5.62

$1.69 + $5.62 = $7.31


So does that mean I take away $7.31(the unused primer and paint) from $185 to end up with $177.69?

$177.69 is my final answer