# The ratio of 7th grade students to 8th grade students in a soccer league is 17:23. If there are 200 students in all, how many are in the 7th grade?

Nov 16, 2016

Let $x$ be the number of 7th grade students and $y$ be the number of 8th grade students.

$\left\{\begin{matrix}17 x = 23 y \\ x + y = 200\end{matrix}\right.$

$y = 200 - x$

$17 x = 23 \left(200 - x\right)$

$17 x = 4600 - 23 x$

$40 x = 4600$

$x = 115$

So, there are $115$ students in 7th grade.

Hopefully this helps!