Difference between revisions of "2024 AMC 8 Problems/Problem 12"
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- C. Ren, Thomas Grover Middle School | - C. Ren, Thomas Grover Middle School | ||
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+ | ==Video Solution 1 (easy to digest) by Power Solve== | ||
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Revision as of 18:25, 25 January 2024
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