求大神解答下数学题

jack3163 · 发表于 2015-7-1 17:26:05

本人数学渣渣，求大神们帮看一下这两道数学

In each term in the sum a1+a2+...+an is either 7 or 77 and the sum equals 350, which of the following could be equal to n?
答案选40

Alice’s take-home pay last year was the same each month, and she saved the same fraction of her take-home pay each month. The total amount of money that she had saved at the end of year was 3 times the amount of that portion of her monthly take-home pay that she did not save. If all the money that she saved last year was from her take-home, what fraction of her take-home pay did she save each month?
答案为1/5

Filter48 · 发表于 2015-7-2 01:57:18

First question: Since the unit digit of each term is 7 and hence only the sum of 10 terms will give you a result of which unit digit is zero (350 in this case), N must be a multiple of 10.

qq342573577 · 发表于 2015-7-2 17:32:08

1. 首先因为an 不是7就是77 ，而总和为350 所以 n肯定是10的倍数（7和77的尾数都是7，而合是350）；如果所有的数都是7的话，n最大为50，但是an需要包括77，所以n只能是10 20 30 40 。接下来就看选项了。
2.假设Alice每月存钱的比例为a（其实带回来多少钱都没差，列出等式都能消掉），根据题目列出等式：12a=3（1-a），解出a=1/5.（12a的意思是去年存钱的总比例，1-a是每月没存的钱的比率）其实等式两边需要乘以每月带回来的钱才是题目要表达的意思，但是可以消掉所以也就无所谓了

求大神解答下数学题

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