2024 AMC 8 Problems/Problem 12: Difference between revisions

Revision as of 14:32, 25 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 $x$ = 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

4 $x$ + 10 = 90.

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

The correct answer is $\textbf{(E)}\ 26$ .

- C. Ren, Thomas Grover Middle School

@@ Line 10: / Line 10: @@
 ==Solution 1==
+Let <math>x</math> = the number of guppies in the first tank.
+Then, we have the following for the number of guppies in the rest of the tanks:
+*<math>x</math> + 1 = the number of guppies in the second tank
+*<math>x</math> + 1 + 2 = the number of guppies in the third tank
+*<math>x</math> + 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
+<math>x</math> + <math>x</math> + 1 + <math>x</math> + 1 + 2 + <math>x</math> + 1 + 2 + 3 = 90.
+Simplifying the equation gives
+<math>x</math> + 10 = 90.
+Solving the resulting equation gives <math>x</math> = 20, so the number of guppies in the fourth tank is 20 + 1 + 2 + 3 = 26.
+The correct answer is <math>\textbf{(E)}\ 26</math>.
+- C. Ren, Thomas Grover Middle School