how much paint is needed to paint the walls of a room 16 x 12 x 10 each gallon covers 400 square feet in each quart covers 100 square feet?

I'm assuming this room has 10 ft ceilings. So the length and width of the room is 16 ft by 12 ft. Two walls are 16*10 = 160 square feet each, so we have 2*160 = 320 sq ft so far. Then we have another two walls that are 12*10 = 120 sq ft, giving an additional 2*120 = 240 sq ft. In total, the walls cover 320+240 = 560 sq ft.

The walls are the lateral surface area of the rectangular block that the room forms. You can use this formula

LSA = 2*(L*H + W*H)

to find the lateral surface area (LSA). In this case, L = 16, W = 12, H = 10.

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Because 1 gallon of paint covers 400 square feet, we can divide the lateral surface area by 400 to find out how many gallons of paint we need.

560/400 = 1.4

round this up to 2 gallons so we have enough paint. If we round to 1 gallon, then we'll be short of the paint needed (we'll be missing that 0.4 of a gallon).

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At the same time, 1 quart of paint covers 100 sq ft, so

560/100 = 5.6

which rounds up to 6. Therefore, we need 6 quarts of paint.

Another way to get this is to multiply 1.4 by 4

1.4*4 = 5.6

because there are 4 quarts in a gallon. This is evident by how 400 is 4 times that of 100.

It might be tempting to round 1.4 up to 2, then multiply by 4 to get 2*4 = 8, which may seem we need 8 quarts instead of 6. This is a bit too much as 6 quarts works also. The value 6 is the smallest whole number of quarts we can buy and still cover all four walls with paint.