# Western State College is 18 years older than Southern State. Western is also 2 1/2 times as old as Southern. How old is each?

Mar 5, 2018

western =

#### Explanation:

use the variable $w$ to represent the age of western state
use the variable $s$ to represent the age of southern state

we need to write 2 equation because we have 2 variables

we know that western state is 18 years older than southern state
$w = 18 + s$

western state is 2.5 times as old as southern
$w = 2.5 s$

solve the system of equations

because $18 + s$ and $2.5 s$ are both equal to $w$, they are also equal to each other
$18 + s = 2.5 s$

solve for $s$ by subtracting $s$ from both sides, then dividing by 1.5
$18 = 1.5 s$
$12 = s$

plug in 12 for $s$ in the first equation
$w = 18 + 12$
$w = 30$