2024 AMC 8 Problems/Problem 12

Rohan keeps a total of 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?

Solution 1

Let = the number of guppies in the first tank.

Then, we have the following for the number of guppies in the rest of the tanks:

• + 1 = the number of guppies in the second tank
• + 1 + 2 = the number of guppies in the third tank
• + 1 + 2 + 3 = the number of guppies in the fourth tank

The number of guppies in all of the tanks combined is 90, so we can write the equation

+ + 1 + + 1 + 2 + + 1 + 2 + 3 = 90.

Simplifying the equation gives

4 + 10 = 90.

Solving the resulting equation gives = 20, so the number of guppies in the fourth tank is 20 + 1 + 2 + 3 = 26.

The correct answer is .

- C. Ren, Thomas Grover Middle School