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John is presently 12 years older than Fred. Four years ago John was twice as old as Fred. How old is each now?

User Colymore
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Final answer:

Using a systems of equations approach, John's and Fred's current ages are found to be 28 and 16 years old, respectively.

Step-by-step explanation:

The problem given is a classic algebra question involving systems of equations. John is presently 12 years older than Fred. If we designate Fred's current age as F and John's current age as J, we can establish the first equation: J = F + 12. Four years ago, John was twice as old as Fred; therefore, we can create a second equation from this information: J - 4 = 2 * (F - 4). Solving these two simultaneous equations will give us the current ages of John and Fred.

From the first equation J = F + 12, we can substitute J in the second equation with F + 12: (F + 12) - 4 = 2 * (F - 4). Simplifying this, F + 8 = 2F - 8, we find that F = 16. Once Fred's age is known, we can easily determine John's age by adding 12: J = 16 + 12, which makes J = 28 years old.

Therefore, Fred is currently 16 years old, and John is 28 years old.

User Martijn Dashorst
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