An art teacher is pouring paint into containers that each hold 2/3 gallon. How many gallons of paint should they buy if they need to fill 8 containers?

Answer as a mixed number = 5 & 1/3 gallons

That rounds up to 6 full gallons assuming s/he cannot buy a fractional amount of a gallon.

Explanation:

We multiply the two numbers given

8*(2/3) = 16/3

Then we can convert this to a mixed number if we wanted

16/3 = (15+1)/3 = 15/3 + 1/3 = 5 + 1/3 = 5 & 1/3

The teacher needs to buy 5 full gallons plus an additional 1/3 of a gallon of paint.

Assuming the teacher cannot buy a fractional amount of paint, s/he will need to bump that value to the nearest whole number. So the art teacher will need to buy 6 gallons of paint. He or she will have leftovers but it's better than coming up short.

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