Maths Olympiad Prep

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Algebra Difficulty 2.9 Junior Find the answer

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?

Pick one

Solution

Let xx 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:

x+1=x + 1 = the number of guppies in the second tank
x+1+2=x + 1 + 2 = the number of guppies in the third tank
x+1+2+3=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=90x + x + 1 + x + 1 + 2 + x + 1 + 2 + 3 = 90.
Simplifying the equation gives
4x+10=904x + 10 = 90.
Solving the resulting equation gives x=20x = 20, so the number of guppies in the fourth tank is 20+1+2+3=2620 + 1 + 2 + 3 = 26.
Therefore, the correct answer is (E) 26\boxed{\textbf{(E)}\ 26}.
- C. Ren
~andliu766 (Minor edits)

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