Question

一个盒子里有 $10$ 磅坚果混合物，其中花生占 $50$ %，腰果占 $20$ %，杏仁占 $30$ %。向盒子中加入另一种坚果混合物，其中花生占 $20$ %，腰果占 $40$ %，杏仁占 $40$ %，得到的新混合物中花生占 $40$ %。现在盒子里有多少磅腰果？

A box contains $10$ pounds of a nut mix that is $50$ percent peanuts, $20$ percent cashews, and $30$ percent almonds. A second nut mix containing $20$ percent peanuts, $40$ percent cashews, and $40$ percent almonds is added to the box resulting in a new nut mix that is $40$ percent peanuts. How many pounds of cashews are now in the box?

$3.5$

$4$

$4.5$

$5$

$6$

答案：B

知识点：混合问题百分数一次方程

难度评级：1020

解答：

第一盒中有 $5$ 磅花生、 $2$ 磅腰果和 $3$ 磅杏仁。加入 $x$ 磅第二种混合物会增加 $0.2x$ 磅花生和 $0.4x$ 磅腰果。

新的花生比例是 $40\%$ ，所以这给出 $5+0.2x=4+0.4x$ ，所以 $x=5$ 。 $\frac{5+0.2x}{10+x}=0.4.$

现在腰果总量为 $2 + 0.4(5) = 4$ 磅。

因此，正确答案是 B。

The first box has $5$ lb peanuts, $2$ lb cashews, and $3$ lb almonds. Adding $x$ pounds of the second mix contributes $0.2x$ lb peanuts and $0.4x$ lb cashews.

The new peanut fraction is $40\%,$ so $\frac{5+0.2x}{10+x}=0.4.$ This gives $5+0.2x=4+0.4x,$ so $x=5.$

The cashews now total $2 + 0.4(5) = 4$ pounds.

Thus, the correct answer is B.

2025 AMC 12A 第 2 题

答案：B

难度评级：1020

解答：

其他年份的第 2 题