AMC12 2011 B

AMC12 2011 B · Q2

AMC12 2011 B · Q2. It mainly tests Averages (mean).

Josanna's test scores to date are $90, 80, 70, 60,$ and $85.$ Her goal is to raise her test average at least $3$ points with her next test. What is the minimum test score she would need to accomplish this goal?

Josanna 到目前为止的测试分数是 $90, 80, 70, 60,$ 和 $85$。她的目标是用下一次测试将平均分提高至少 $3$ 分。她需要的最低测试分数是多少？

(A) 80 80

(B) 82 82

(D) 90 90

(E) 95 95

Answer

Correct choice: (E)

正确答案：（E）

Solution

Take the average of her current test scores, which is \[\frac{90+80+70+60+85}{5} = \frac{385}{5} = 77\] This means that she wants her test average after the sixth test to be $80.$ Let $x$ be the score that Josanna receives on her sixth test. Thus, our equation is \[\frac{90+80+70+60+85+x}{6} = 80\] \[385+x = 480\] \[x = \boxed{95 \textbf{(E)}}\]

先求她当前测试分数的平均值： \[\frac{90+80+70+60+85}{5} = \frac{385}{5} = 77\] 这意味着她希望第六次测试后的平均分为 $80$。设 Josanna 第六次测试的分数为 $x$，则 \[\frac{90+80+70+60+85+x}{6} = 80\] \[385+x = 480\] \[x = \boxed{95 \textbf{(E)}}\]

Topics

AR.006 Averages (mean)