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

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==Solution 1==
 
==Solution 1==
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Let <math>x</math> = the number of guppies in the first tank.
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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
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 +
4<math>x</math> + 10 = 90.
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 +
Solving the resulting equation gives <math>x</math> = 20, so the number of guppies in the fourth tank is 20 + 1 + 2 + 3 = 26.
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The correct answer is <math>\textbf{(E)}\ 26</math>.
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 +
- C. Ren, Thomas Grover Middle School

Revision as of 14:32, 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?

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

Solution 1

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:

  • $x$ + 1 = the number of guppies in the second tank
  • $x$ + 1 + 2 = the number of guppies in the third tank
  • $x$ + 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

$x$ + $x$ + 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

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