2024 AMC 8 第 12 题

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所有题目均经美国数学协会(MAA)官方合法授权使用。

12.

Rohan 在四个鱼缸中共养了九十条孔雀鱼。

• 第二个鱼缸比第一个多一条孔雀鱼。

• 第三个鱼缸比第二个多两条孔雀鱼。

• 第四个鱼缸比第三个多三条孔雀鱼。

第四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 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?

2020

2121

2323

2424

2626

答案:E
知识点:一次方程
难度评级:980
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文字解答:

设第一个鱼缸有 xx 条,则四个鱼缸分别有 xxx+1x+1x+3x+3x+6x+6 条。由总数可得 x+x+1+x+3+x+6=90x + x + 1 + x + 3 + x + 6 = 90 4x+10=904x+10=90 x=20.x=20.

题目问的是第四个鱼缸的数量,不是第一个鱼缸。因此第四个鱼缸有 x+6=20+6=26x+6=20+6=26 条。

正确答案是 E

Let xx be the number of guppies in the 1st tank. Hence, there are x+1x+1 guppies in the 2nd tank, x+3x+3 guppies in the 3rd tank, and x+6x+6 guppies in the 4th tank. We then use the fact that there are a total of 90 guppies in the 4 tanks to find xx: x+x+1+x+3+x+6=90x + x + 1 + x + 3 + x + 6 = 90 4x+10=904x+10=90 x=20.x=20.

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

Thus, E is the correct answer.

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