AMC10 2010 B

AMC10 2010 B · Q9

AMC10 2010 B · Q9. It mainly tests Manipulating equations.

Lucky Larry’s teacher asked him to substitute numbers for $a,b,c,d,$ and $e$ in the expression $a-(b-(c-(d+e)))$ and evaluate the result. Larry ignored the parentheses but added and subtracted correctly and obtained the correct result by coincidence. The numbers Larry substituted for $a,b,c,$ and $d$ were 1, 2, 3, and 4, respectively. What number did Larry substitute for $e$?

幸运拉里的老师让他在表达式 $a-(b-(c-(d+e)))$ 中代入数字代替 $a,b,c,d,$ 和 $e$ 并计算结果。拉里忽略了括号但加减正确，碰巧得到了正确结果。拉里代入 $a,b,c,$ 和 $d$ 的数字分别是 1、2、3 和 4。那么拉里代入 $e$ 的数字是多少？

(A) -5 -5

(B) -3 -3

(D) 3 3

(E) 5 5

Answer

Correct choice: (D)

正确答案：（D）

Solution

The correct answer was $1-(2-(3-(4+e)))=1-2+3-4-e=-2-e$. Larry’s answer was $1-2-3-4+e=-8+e$. Therefore $-2-e=-8+e$, so $e=3$.

正确答案是 $1-(2-(3-(4+e)))=1-2+3-4-e=-2-e$。拉里的答案是 $1-2-3-4+e=-8+e$。因此 $-2-e=-8+e$，所以 $e=3$。

Topics

AL.016 Manipulating equations