If 1/3 gallon of paint covers 1/6 of a wall then how many quarts of paint of paint are needed for the entire wall?

The answer to your question is 8 quarts

Step-by-step explanation:

Data

1/3 gallon  --  1/6 of a wall

the number of quarts = ?

Process

1.- Use proportions to calculate the gallons of paint.

               1/3 of a gallon 1/6 of a wall

                 x                      1 (all the wall)

                      x = (1 x 1/3) / 1/6

-Simplification

                      x = 1/3 / 1/6

                      x = 6/3

                      x = 2 gallons

2.- Convert gallons to quarts

                      1 gallons 4 quarts

                      2 gallons  x

                         x = (2 x 4) / 1

                         x = 8 / 1

                         x = 8 quarts

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is