AMC12 2010 B

AMC12 2010 B · Q5

AMC12 2010 B · Q5. 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 parenthese but added and subtracted correctly and obtained the correct result by coincidence. The number Larry substituted for $a$, $b$, $c$, and $d$ were $1$, $2$, $3$, and $4$, respectively. What number did Larry substitute for $e$?

Lucky Larry 的老师让他在表达式 $a-(b-(c-(d+e)))$ 中用数字替换 $a$、$b$、$c$、$d$ 和 $e$ 并计算结果。Larry 忽略了括号但正确地进行了加减法，并碰巧得到了正确结果。Larry 分别用 $1$、$2$、$3$ 和 $4$ 替换了 $a$、$b$、$c$ 和 $d$。Larry 用什么数字替换了 $e$？

(A) -5 -5

(B) -3 -3

(D) 3 3

(E) 5 5

Answer

Correct choice: (D)

正确答案：（D）

Solution

We simply plug in the numbers \[1 - 2 - 3 - 4 + e = 1 - (2 - (3 - (4 + e)))\] \[-8 + e = -2 - e\] \[2e = 6\] \[e = 3 \;\;(D)\]

直接代入： \[1 - 2 - 3 - 4 + e = 1 - (2 - (3 - (4 + e)))\] \[-8 + e = -2 - e\] \[2e = 6\] \[e = 3 \;\;(D)\]

Topics

AL.016 Manipulating equations