Let's use variables:
* G: Number of goldfish
* M: Number of mollies
* P: Number of guppies
Set up equations based on the given information:
* "The tank contains 1 2 as many goldfish as mollies"
This means G = (1/2)M
* "There are 6 more guppies than mollies"
This means P = M + 6
* "The total number of fish is 22"
This means G + M + P = 22
Now we can solve for the number of each type of fish:
1. Substitute the expressions for G and P from the first two equations into the third equation:
(1/2)M + M + (M + 6) = 22
2. Simplify the equation:
(5/2)M + 6 = 22
3. Solve for M:
(5/2)M = 16
M = 16 * (2/5) = 6.4
Since you can't have a fraction of a fish, we'll round down to 6 mollies.
4. Find G:
G = (1/2) * 6 = 3 goldfish
5. Find P:
P = 6 + 6 = 12 guppies
Therefore, the fish tank contains 3 goldfish, 6 mollies, and 12 guppies.