Jack's room has $27 \mathrm{~m}^{2}$ of wall and ceiling area. To paint it, Jack can use 1 can of paint, but 1 liter of paint would be left over, or 5 gallons of paint, but 1 liter would also be left over, or 4 gallons plus 2.8 liters of paint.

a) What is the ratio between the volume of a can and the volume of a gallon?

b) What is the volume of a gallon?

c) What is the area that Jack can paint with 1 liter of paint, that is, what is the yield of the paint?
Solution

a) If using 1 can or 5 gallons leaves the same amount of paint, then both have the same volume, as they cover the same area. Therefore, the ratio of their volumes (1 can to 5 gallons) is $\frac{1}{5}$.

b) We have that 5 gallons minus 1 liter is equivalent to 4 gallons plus 2.8 liters, which means 1 gallon is 3.8 liters.

c) It takes 5 * 3.8 - 1 = 18 liters to paint the $27 m^{2}$ of Jack's room, which means $\frac{27}{18}=1.5 \mathrm{~m}^{2} / \ell$.