AMC8 2024

AMC8 2024 · Q12

AMC8 2024 · Q12. It mainly tests Linear equations, Arithmetic misc.

Rohan keeps 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?

罗汉在4个鱼缸里养了90条孔雀鱼。 - 第2个鱼缸比第1个鱼缸多1条孔雀鱼。 - 第3个鱼缸比第2个鱼缸多2条孔雀鱼。 - 第4个鱼缸比第3个鱼缸多3条孔雀鱼。第4个鱼缸里有多少条孔雀鱼？

(A) \ 20 \ 20

(B) \ 21 \ 21

(D) \ 24 \ 24

(E) \ 26 \ 26

Answer

Correct choice: (E)

正确答案：（E）

Solution

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 the second tank is $x+1$ - The number of guppies in the third tank is $x+1+2$ - The number of guppies in the fourth tank is $x+1+2+3$ 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 $20+1+2+3 = \boxed{\textbf{(E)}\ 26}$.

设 $x$ 表示第一个鱼缸中的孔雀鱼数量。则其余鱼缸的数量如下： - 第二个鱼缸：$x+1$ - 第三个鱼缸：$x+1+2$ - 第四个鱼缸：$x+1+2+3$ 所有鱼缸总数为 90，因此方程为 \[(x)+(x+1)+(x+1+2)+(x+1+2+3) = 90.\] 简化得 \[4x + 10 = 90.\] 解得 $x = 20$，所以第四个鱼缸有 $20+1+2+3 = \boxed{\textbf{(E)}\ 26}$ 条。

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