A cooler of Gatorade is filled at the beginning of a football game. During the first quarter, the players drank 1 / 4 of the Gatorade. During the second quarter, they drank 1 / 2 of the remaining Gatorade. During the third quarter, the players drank 1/ 3 of the liquid that remained after halftime. If 10 cups are left at the beginning of the fourth quarter, how much Gatorade did the cooler originally hold?

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

y = 3x+4

step-by-step explanation:

to find the slope

slope = (y2-y1)/ (x2-x1)

    = (-8-4)/ (-4-0)

    = -12/-4

  = 3

using the slope intercept form of a line

y= mx+b

we know the slope is 3

we know the y intercept is 4 ( the point where it crosses the y axis or x=0)

y = 3x+4

just keep asking questions until you have a better understanding.

step-by-step explanation:

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