Population of linton is 12 times as great as the population of ellmore. the combined population of both towns is 9,646 people. what is the population of linton?

Let "L" represent the population of Linton
and "E" represent the population of Ellmore

12 times E = L
because "Linton is 12 times as great as .. Ellmore"

then  E + L = 9646
because "the combined population is 9646"

since  L = 12*E
we can plug that into the other equation and get:
E + 12*E = 9646
13*E = 9646   [by adding like terms]
E = 742   [by divided both sides by 13]

so now we have E
we can plug that back into the 1st equation to get L
12*(742) = L
L = 8904

so Population of Linton = 8904
and the Population of Ellmore = 742

10.4 is the answer for you