If one quart of paint is exactly enough for two coats of paint on a 9-foot by 10-foot wall, how many quarts of paint are needed to apply one coat of paint to a 10-foot by 12-foot wall? Express your answer as a common fraction

2/3 quart

Step-by-step explanation:

The 10 by 12 ft wall has an area of 120 ft^2.  The 9 by 10 ft wall has an area of 90 ft^2.

Thus, the following equation of ratios provides us with the

  90         (1/2)

=

 120            x

or 3/4 = 1/(2x), or

6x = 4.  Thus, x = 4/6 or 2/3.

2/3 of a quart would be enough for one coat on the 10 by 12 ft wall.  Note that only 1/2 of a quart would suffice for one coat on a 9 by 10 ft wall (for comparison).