Final answer:
Lilly is 12 years old and John is 11 years old.
Step-by-step explanation:
Let's represent Lilly's age as L and John's age as J.
According to the question, John is 1 year younger than Lilly. So, we can represent their ages as:
L = J + 1
The sum of their ages is given as 23 years, so:
L + J = 23
Substituting the first equation into the second equation:
(J + 1) + J = 23
Combining like terms:
2J + 1 = 23
Subtracting 1 from both sides:
2J = 22
Dividing both sides by 2:
J = 11
Substituting this value of J back into the first equation:
L = 11 + 1 = 12
So, Lilly is 12 years old and John is 11 years old.