Question

Rohan 在 $4$ 个鱼缸中共养了 $90$ 条孔雀鱼。

• 第 $2$ 个鱼缸比第 $1$ 个多 $1$ 条孔雀鱼。

• 第 $3$ 个鱼缸比第 $2$ 个多 $2$ 条孔雀鱼。

• 第 $4$ 个鱼缸比第 $3$ 个多 $3$ 条孔雀鱼。

第 $4$ 个鱼缸中有多少条孔雀鱼？

Rohan keeps a total of $90$ guppies in $4$ fish tanks.

• There is $1$ more guppy in the $2$ nd tank than in the $1$ st tank.

• There are $2$ more guppies in the $3$ rd tank than in the $2$ nd tank.

• There are $3$ more guppies in the $4$ th tank than in the $3$ rd tank.

How many guppies are in the $4$ th tank?

$20$

$21$

$23$

$24$

$26$

答案：E

知识点：一次方程

难度评级：980

小提示：

用第一个鱼缸的数量表示每个鱼缸

Write each tank amount in terms of the first tank

大提示：

第四个鱼缸比第一个多 $6$ 条

The fourth tank has $6$ more guppies than the first

视频讲解：

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文字解答：

设第 $1$ 个鱼缸有 $x$ 条孔雀鱼，则第 $2$ 个鱼缸有 $x+1$ 条，第 $3$ 个鱼缸有 $x+3$ 条，第 $4$ 个鱼缸有 $x+6$ 条。由 $4$ 个鱼缸共有 $90$ 条孔雀鱼求 $x$ ： $x + x + 1 + x + 3 + x + 6 = 90$ $4x+10=90$ $x=20\text{。}$

题目问的是第 $4$ 个鱼缸的数量，不是第 $1$ 个鱼缸。因此第 $4$ 个鱼缸有 $x+6=20+6=26$ 条。

正确答案是 E。

Let $x$ be the number of guppies in the $1$ st tank. Hence, there are $x+1$ guppies in the $2$ nd tank, $x+3$ guppies in the $3$ rd tank, and $x+6$ guppies in the $4$ th tank. We then use the fact that there are a total of $90$ guppies in the $4$ tanks to find $x$ : $x + x + 1 + x + 3 + x + 6 = 90$ $4x+10=90$ $x=20.$

Note that we are not yet done since we are asked for the number of guppies in the $4$ th tank and not the $1$ st. There are $x+6=20+6=26$ guppies in the $4$ th tank.

Thus, E is the correct answer.

2024 AMC 8 第 12 题