2024 AMC 8 Problem 12

Below is the video solution and professionally curated solution for Problem 12 of the 2024 AMC 8, 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 of the real AMC 8, AMC 10, AMC 12, and AIME problems in our complete solution collection are used with official legal permission of the Mathematical Association of America (MAA).

Concepts:linear equation

Difficulty rating: 980

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

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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