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

Revision as of 13:16, 26 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

$4x + 10 = 90$ .

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

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

- C. Ren, Thomas Grover Middle School

@@ Line 14: / Line 14: @@
 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 + 1 =</math> the number of guppies in the second tank
-*<math>x</math> + 1 + 2 = the number of guppies in the third tank
+*<math>x + 1 + 2 =</math> the number of guppies in the third tank
-*<math>x</math> + 1 + 2 + 3 = the number of guppies in the fourth tank
+*<math>x + 1 + 2 + 3 =</math> 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.
+<math>x + x + 1 + x + 1 + 2 + x + 1 + 2 + 3 = 90</math>.
 Simplifying the equation gives
-<math>x</math> + 10 = 90.
+<math>4x + 10 = 90</math>.
-Solving the resulting equation gives <math>x</math> = 20, so the number of guppies in the fourth tank is 20 + 1 + 2 + 3 = 26.
+Solving the resulting equation gives <math>x = 20</math>, so the number of guppies in the fourth tank is <math>20 + 1 + 2 + 3 = 26</math>.
 The correct answer is <math>\textbf{(E)}\ 26</math>.