Jane's aquarium contains goldfish, turtles, and snails. There are 16 legs, 10 shells, and 36 eyes in the aquarium. How many creatures of each type are in the aquarium? (Hint: Snails have two eyes, one shell, and one leg.)
Since there are 36 eyes and all the animals have 2 eyes, there are 18 animals total. Fish have no legs. Since there are 10 shells, the combined number of turtles and snails = 10. This means that there are 8 fish. The ten shelled animals share 16 legs. How can these 10 animals share these 16 legs, some with 4 and others with one?
Let's assume the number of goldfish in the aquarium is G, the number of turtles is T, and the number of snails is S.
From the given information, we can derive the following equations:
1. The total number of legs in the aquarium can be written as:
Legs from goldfish + Legs from turtles + Legs from snails = 16
Since goldfish and turtles have no legs, the equation becomes:
0 + 0 + (S x 1) = 16
S = 16/1
S = 16
2. The total number of shells in the aquarium can be written as:
Shells from turtles + Shells from snails = 10
T + S = 10
3. The total number of eyes in the aquarium can be written as:
Eyes from goldfish + Eyes from turtles + Eyes from snails = 36
(G x 2) + (T x 2) + (S x 2) = 36
2G + 2T + 2S = 36
G + T + S = 36/2
G + T + S = 18
Now, we can solve these equations simultaneously to find the values of G, T, and S.
Using the second and third equations, we can substitute the value of S:
T + 16 = 10
T = 10 - 16
T = -6
Since we can't have negative turtles, it means there must be an error in the problem or information provided.
Please provide the correct information to proceed.
To find the number of creatures of each type in the aquarium, we need to set up a system of equations based on the given information.
Let's use the variables:
- Let g represent the number of goldfish in the aquarium.
- Let t represent the number of turtles in the aquarium.
- Let s represent the number of snails in the aquarium.
Based on the information given:
- Goldfish have zero legs, zero shells, and zero eyes.
- Turtles have four legs, one shell, and two eyes.
- Snails have one leg, one shell, and two eyes.
Now let's set up the equations:
1. Legs:
The total number of legs can be calculated by multiplying the number of goldfish (g) by 0 (since goldfish have zero legs), adding the number of turtles (t) multiplied by 4 (since turtles have four legs), and adding the number of snails (s) multiplied by 1 (since snails have one leg):
0g + 4t + 1s = 16
2. Shells:
The total number of shells can be calculated by adding the number of turtles (t) multiplied by 1 (since turtles have one shell), and adding the number of snails (s) multiplied by one (since snails have one shell):
0g + t + s = 10
3. Eyes:
The total number of eyes can be calculated by adding the number of turtles (t) multiplied by 2 (since turtles have two eyes), and adding the number of snails (s) multiplied by 2 (since snails have two eyes):
0g + 2t + 2s = 36
So, the system of equations is:
0g + 4t + 1s = 16
0g + t + s = 10
0g + 2t + 2s = 36
Now, we can solve this system of equations to find the values of g, t, and s.