SOLUTION: A ten-gallon aquarium is 3 inches higher than it is wide. Its length is 21 inches., and its volume is 2730 inches cubed. What are the height and width of the aquarium?

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Start with the formula for the volume of a rectangular prism (this is the shape of the aquarium): V = L*W*H (That's Length * Width * Height)
L = 21 inches
H = W + 3
V = (21)(W)(W+3) = 2730 cubic inches.
(21)(W^2 + 3W) = 2730 Cubic inches. Divide both sides by 21.
W^2 + 3W = 130 Subtract 130 from both sides.
W^2 + 3W - 130 = 0 Solve the quadratic by factoring.
(W + 13)(W - 10) = 0 Apply the zero products principle.
W + 13 = 0, W = -13 Discard this solution as negative width is not meaningful.
W - 10 = 0, W = 10 The width of the aquarium is 10 inches.
H = W + 3
H = 13 The height of the aquarium is 13 inches.
Check: Volume, V = (21")(10")(13") = 2730 cubic inches.