AMC10 2017 B

AMC10 2017 B · Q5

AMC10 2017 B · Q5. It mainly tests Systems of equations, Word problems (algebra).

Camilla had twice as many blueberry jelly beans as cherry jelly beans. After eating 10 pieces of each kind, she now has three times as many blueberry jelly beans as cherry jelly beans. How many blueberry jelly beans did she originally have?

卡米拉蓝莓果冻豆的数量是樱桃果冻豆的两倍。吃掉每种10颗后，她现在蓝莓果冻豆的数量是樱桃果冻豆的三倍。她原来有多少蓝莓果冻豆？

(A) 10 10

(B) 20 20

(D) 40 40

(E) 50 50

Answer

Correct choice: (D)

正确答案：（D）

Solution

Suppose Camilla originally had $b$ blueberry jelly beans and $c$ cherry jelly beans. After eating 10 pieces of each kind, she now has $b - 10$ blueberry jelly beans and $c - 10$ cherry jelly beans. The conditions of the problem are equivalent to the equations $b = 2c$ and $b - 10 = 3(c - 10)$. Then $2c - 10 = 3c - 30$, which means that $c = 20$ and $b = 2 \cdot 20 = 40$.

假设卡米拉原来有$b$颗蓝莓果冻豆和$c$颗樱桃果冻豆。吃掉每种10颗后，她现在有$b - 10$颗蓝莓和$c - 10$颗樱桃。题目条件等价于方程$b = 2c$和$b - 10 = 3(c - 10)$。则$2c - 10 = 3c - 30$，即$c = 20$，$b = 2 \cdot 20 = 40$。

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