## ParthKohli 3 years ago I found this easy problem in the grade 8th entrance exam... try it :-) Let $$\large x_1, x_2, x_3 \cdots x_n$$ be a sequence such that $$\large \sum \limits_{i = 1}^{n} (x_i - 3) = 170$$ and $$\large \sum \limits_{i = 1}^{n} (x_i - 6) = 50$$. What is the value of $$n$$?

1. goformit100

0k ?

2. anonymous

Okay, it's not a hard problem, but it is tedious and requires knowledge about summations that is barely touched in many algebra 2 classes.

3. anonymous

Multiply the first equation by $$-2$$ and then add it to the second equation.

$$\sum \limits_{i=1}^nx_i=p\\ \sum\limits_{i=1}^nx_i-\sum\limits_{i=1}^n3=170 \implies p-3n=170\qquad (1)\\ \sum\limits_{i=1}^nx_i-\sum\limits_{i=1}^n6=50\implies p-6n=50 \qquad(2)$$ (1)-(2) 3n=120 => n=40

5. ParthKohli