2024 AMC 8
Complete problem set with solutions and individual problem pages
Rohan keeps 90 guppies in 4 fish tanks.
- There is 1 more guppy in the 2nd tank than in the 1st tank.
- There are 2 more guppies in the 3rd tank than in the 2nd tank.
- There are 3 more guppies in the 4th tank than in the 3rd tank.
How many guppies are in the 4th tank?
- A.
- B.
- C.
- D.
- E.
Solution 1
Let denote the number of guppies in the first tank.
Then, we have the following for the number of guppies in the rest of the tanks:
- The number of guppies in the second tank is
- The number of guppies in the third tank is
- The number of guppies in the fourth tank is
The number of guppies in all of the tanks combined is 90, so we can write the equation
Simplifying the equation gives
Solving the resulting equation gives , so the number of guppies in the fourth tank is .
Solution 2
Suppose there are no guppies in the first tank. Then, the number of guppies in the other tanks are and or guppies in total. We need to add guppies into tanks or guppies in each tank, so the number of guppies in the fourth tank is
