AMC10 2025 A

AMC10 2025 A · Q2

AMC10 2025 A · Q2. It mainly tests Mixture / concentration.

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?

一个盒子含有 10 磅坚果混合物，其中 50% 是花生，20% 是腰果，30% 是杏仁。将另一种坚果混合物（20% 花生，40% 腰果，40% 杏仁）加入盒子后，新混合物中花生比例为 40%。现在盒子中腰果有多少磅？

(A) 3.5 3.5

(B) 4 4

(D) 5 5

(E) 6 6

Answer

Correct choice: (B)

正确答案：（B）

Solution

We are given $0.2(10) = 2$ pounds of cashews in the first box. Denote the pounds of nuts in the second nut mix as $x.$ \[5 + 0.2x = 0.4(10 + x)\] \[0.2x = 1\] \[x = 5\] Thus, we have $5$ pounds of the second mix. \[0.4(5) + 2 = 2 + 2 = \boxed{\text{(B) }4}\]

第一个盒子中有 $0.2(10) = 2$ 磅腰果。设第二种坚果混合物的磅数为 $x$。 \[5 + 0.2x = 0.4(10 + x)\] \[0.2x = 1\] \[x = 5\] 因此，有 5 磅第二种混合物。 \[0.4(5) + 2 = 2 + 2 = \boxed{\text{(B) }4}\]

Topics

AR.009 Mixture / concentration