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 9090 guppies in 44 fish tanks.

• There is 11 more guppy in the 22nd tank than in the 11st tank.

• There are 22 more guppies in the 33rd tank than in the 22nd tank.

• There are 33 more guppies in the 44th tank than in the 33rd tank.

How many guppies are in the 44th tank?

2020

2121

2323

2424

2626

Answer: E
Concepts:linear equation
Difficulty rating: 980
Small Hint:

Write each tank amount in terms of the first tank

Big Hint:

The fourth tank has 66 more guppies than the first

Video solution:
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Written solution:

Let xx be the number of guppies in the 11st tank. Hence, there are x+1x+1 guppies in the 22nd tank, x+3x+3 guppies in the 33rd tank, and x+6x+6 guppies in the 44th tank. We then use the fact that there are a total of 9090 guppies in the 44 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 44th tank and not the 11st. There are x+6=20+6=26x+6=20+6=26 guppies in the 44th tank.

Thus, E is the correct answer.

Problem 11#11
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