Can exemplar problems have a remaining number left

In this problem, we can assign X to the son’s age and Y to the father’s.

We know that a father is 3 times as old as his son.

Therefore, we can create the equation 3X=Y.

We must now create a second equation from the remaining information, being “In 12 years he will be twice as old as his son”. We know we can add 12 years, along with including 2X in the equation.

The equation that we can gather from this second piece of information will be Y=2X+12. This is because the father’s age, in 12 year’s time, will be twice that of the child.

Now we have our two equations:

Y=3X

Y=2X+12

Because both equations are set equal to the age of the father, we can use the substitution method to solve in terms of the son’s age, as follows:

3X = 2X+12

Now we subtract 2X from each side to isolate the variable:

X=12

The son’s age is therefore 12 years old. Should we plug that age back into our first equation, we get Y=3(12) or Y=36.

The father’s present age is 36, while the son’s present age is 12.