2024 AMC 8 Problem 12

Attempt Problem 12 of the 2024 AMC 8 below, then check your answer against the video solution and professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2024 AMC 8 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

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?

2020

2121

2323

2424

2626

Answer: E
Concepts:linear equation
Difficulty rating: 980
Video solution:
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Written solution:

Let xx be the number of guppies in the 1st tank. Hence, there are x+1x+1 guppies in the 2nd tank, x+3x+3 guppies in the 3rd tank, and x+6x+6 guppies in the 4th tank. We then use the fact that there are a total of 90 guppies in the 4 tanks to find xx: x+x+1+x+3+x+6=90x + x + 1 + x + 3 + x + 6 = 90 4x+10=904x+10=90 x=20.x=20.

Note that we are not yet done since we are asked for the number of guppies in the 4th tank and not the 1st. There are x+6=20+6=26x+6=20+6=26 guppies in the 4th tank.

Thus, E is the correct answer.

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