From each sentence, we can create a math equation:
The sum of the ages of Jesse and Sophia is 111 years.
J + S = 111
8 years ago, Jesse's age was 4 times Sophia's age.
(J-8) = 4(S-8)
Now we have 2 equations and 2 unknowns, so we can solve this system of equation by solving for one variable in terms of the other.
J = 111-S
substitute for J in the 2nd equation:
(111 - S) - 8 = 4(S - 8)
103 - S = 4S - 32
add S to both sides to get all the S terms together:
103 - S + S = 4S - 32 + S.
103 = 5S - 32
add 32 to both sides to get the S term alone
103 + 32 = 5S - 32 + 32
135 = 5S
divide by 5 to get S
S = 135/5 = 27
Sophie is 27.
Plug S back into the 1st equation to find Jesse's age:
J = 111 - S
= 111 - 27
= 84
Jesse is 84 years old now.
This is reasonable, since we know Jesse was 4x older than Sophie a few years ago.
