Mai has a new aquarium. The tank is in the shape of a rectangular prism,
48in
long,
36in
wide, and
24in
deep. She plans to raise fish and sell them to a local pet store. The pet store will inspect the aquarium to make sure that the fish are being kept in a healthful environment. One of the main concerns is that each fish has enough water. Mai looks up the amount of water needed for the species of fish she plans to raise. She finds the answer, but it is given in cubic feet.
(a) Find the volume of water that the tank holds in cubic feet. Use the table of conversion facts, as needed.
ft3
(b) The particular species Mai plans to raise requires at least
1.4ft3
of water per fish. If there is any amount less than this, no matter how much less, the pet store will not accept Mai's fish. What is the largest whole number of fish that she can keep in the aquarium?
fish
(c) The pet store will pay
$7.99
for each fish. If she fully populates her aquarium and sells all the fish, how much money will she collect?
(a) The volume of the tank in cubic feet is:
V = l x w x h
V = 48in x 36in x 24in
V = 41,472 cubic inches
To convert cubic inches to cubic feet, we need to divide by 12^3 (since there are 12 inches in a foot):
V = 41,472 / 12^3
V ≈ 24 cubic feet
Therefore, the tank holds approximately 24 cubic feet of water.
(b) To find the largest whole number of fish she can keep, we need to divide the volume of the tank by the required volume of water per fish:
N = V / 1.4
N = 24 / 1.4
N ≈ 17.14
Since she can't have a fraction of a fish, the largest whole number of fish she can keep is 17.
(c) If she sells all 17 fish at $7.99 each, she will collect:
17 x $7.99 = $135.83
Therefore, she will collect $135.83 if she fully populates her aquarium and sells all the fish.
To answer these questions, we need to perform some calculations. Let's go step by step.
(a) To find the volume of water that the tank holds in cubic feet, we need to multiply the length, width, and depth of the tank. The dimensions are given in inches, so we first convert them to feet:
Length = 48in = 48in / 12in/ft = 4ft
Width = 36in = 36in / 12in/ft = 3ft
Depth = 24in = 24in / 12in/ft = 2ft
Volume = Length * Width * Depth = 4ft * 3ft * 2ft = 24ft³
Therefore, the tank holds 24 cubic feet of water.
(b) The species Mai plans to raise requires at least 1.4 cubic feet of water per fish. To find the maximum number of fish she can keep in the aquarium, we divide the volume of the tank by the required volume per fish:
Number of fish = Volume of the tank / Required volume per fish = 24ft³ / 1.4ft³ = 17.14
Since we can only have whole numbers of fish, Mai can keep a maximum of 17 fish in the aquarium.
(c) If she fully populates her aquarium and sells all the fish, the pet store will pay $7.99 for each fish. To calculate the total amount of money, we multiply the number of fish by the price per fish:
Total money collected = Number of fish * Price per fish = 17 * $7.99 = $135.83
Therefore, Mai will collect $135.83 if she sells all the fish.