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?

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Answer 1 · 2018-03-05T06:12:25

western =

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#