Answer:
Step-by-step explanation:
To create a system of inequalities, write an inequality to model each condition that must be satisfied in the given situation.
It is given that x represents the area of the base of the barrel in square feet and y represents the volume of the pump in cubic feet.
Write an inequality to represent the amount of water that the barrel needs to hold after the pump is inserted. To find the volume of the barrel, multiply the area of the base by the height of the barrel. Then subtract the volume that will be taken up by the pump from that amount.
x(x-4) - y ≤ 90
To find the cost of the supplies for the barrel, find the surface area by multiplying the perimeter of the base by the height of the barrel and then adding the area of the base. Since there is no top, the area of the base only needs to be added once. Then, multiply the cost per square foot by the surface area.
To find the cost of the pump, multiply the cost per square foot of the pump by its volume.
Write an inequality representing the total cost. The cost must be less than or equal to $1,100.
8(x(x-4)+x) + 50y ≤ 1,100
Combining both of the inequalities gives the following system of inequalities.
x(x-4) - y ≤ 90
8(x(x-4)+x) + 50y ≤ 1,100
