Question

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?

Answer 1

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=2.5s`

solve the system of equations

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

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

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