Final answer:
To determine John's age, we create two equations based on the given information: C = 3J and C - 20 = 5(J - 20). Solving these equations algebraically reveals that John is 40 years old.
Step-by-step explanation:
The question presented involves solving an algebraic problem related to the ages of Carol and John. We need to establish two equations based on the information given:
Carol is 3 times as old as John today.
Twenty years ago, Carol was five times as old as John.
Let's define Carol's current age as C and John's current age as J.
From the first piece of information, we have the equation: C = 3J.
From the second piece of information, we can write: C - 20 = 5(J - 20).
Substitute the first equation into the second to have one equation with one unknown:
3J - 20 = 5J - 100
Now we solve for John's age:
100 - 20 = 5J - 3J
80 = 2J
J = 40
Therefore, John's current age is 40 years old.