Presently: 2020
Let Kevin’s age be kevinPresentAge and Timothy’s age be timothyPresentAge for the present year 2020. The statement states that “Kevin is 6 years older than Timothy”
kevinPresentAge=timothyPresentAge+6
4 years ago: 2016
Let Kevin’s age be kevinOldAge and Timothy’s age be timothyOldAge for the old year of 2016. The statement states that “Kevin was twice as old as Timothy”
2. kevinOldAge=2∗timothyOldAge
Now we have two equations and we have to solve it simultaneously. But unfortunately, the variable names are not the same. kevinPresentAge is not the same as kevinOldAge . So what can be done?
The relationship between kevinOldAge and kevinPresentAge is the difference between the years. In the statement, it is given as 4 years ago, which is why I choose the year 2020 and 2016 for the explanation. Therefore:
3. kevinOldAge=kevinPresentAge−4
4. timothyOldAge=timothyPresentAge−4
So now, we substitute equation 3 and 4 into equation 2 and it would become:
2. kevinPresentAge−4=2∗(timothyPresentAge−4)
So now, we will solve equation 1 and 2 since they have the same variables. But before that, I’ll like to change the variable names to something more simple and mathematical. Let kevinPresentAge=x while timothyPresentAge=y . Please don’t ask me y I did that (just kidding). So the equation would now look like:
1. x=y+6
2. x−4=2∗(y−4)
There are a number of ways to solve simultaneous equation but let’s use substitution method. Substitute equation x in equation 1 into equation 2 and it would become:
y+6−4=2∗(y−4)
y+2=2y−8
2y−y=2+8
y=10
Now let’s go back to equation 1 with the solved y.
x=10+6
x=16
So there you have it.
x=kevinPresentAge=16
y=timothyPresentAge=10