Difference between revisions of "2024 AMC 8 Problems/Problem 12"

Revision as of 06:55, 27 January 2024

Rohan keeps a total of 90 guppies in 4 fish tanks.

How many guppies are in the 4th tank?

$\textbf{(A)}\ 20 \qquad \textbf{(B)}\ 21 \qquad \textbf{(C)}\ 23 \qquad \textbf{(D)}\ 24 \qquad \textbf{(E)}\ 26$

Let $x$ denote the number of guppies in the first tank.

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

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

$x + x + 1 + x + 1 + 2 + x + 1 + 2 + 3 = 90$ .

Simplifying the equation gives

$4x + 10 = 90$ .

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

Therefore, the correct answer is $\boxed{\textbf{(E)}\ 26}$ .

- C. Ren, Thomas Grover Middle School ~andliu766 (Minor edits)

Suppose, there is no guppies in the first tank. The numbers of guppies in another tanks are $1,3,$ and $6,$ totally $10$ guppies.

We need to add $90 - 10 = 80$ guppies into $4$ tanks or $20$ guppies in each tank.

So the number of guppies in the fourth tank is $20 + 6 = \boxed{\textbf{(E)}\ 26}.$

vladimir.shelomovskii@gmail.com, vvsss

~NiuniuMaths

@@ Line 33: / Line 33: @@
 - C. Ren, Thomas Grover Middle School
 ~andliu766 (Minor edits)
+==Solution 2==
+Suppose, there is no guppies in the first tank. The numbers of guppies in another tanks are <math>1,3,</math> and <math>6,</math> totally <math>10</math> guppies.
+We need to add <math>90 - 10 = 80</math> guppies into <math>4</math> tanks or <math>20</math> guppies in each tank.
+So the number of guppies in the fourth tank is <math>20 + 6 = \boxed{\textbf{(E)}\ 26}.</math>
+'''vladimir.shelomovskii@gmail.com, vvsss'''
 ==Video Solution 1 (easy to digest) by Power Solve==

2024 AMC 8 (Problems • Answer Key • Resources)
Preceded by Problem 11	Followed by Problem 13
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All AJHSME/AMC 8 Problems and Solutions