Answer: Five years ago Randy was 8 years old
Step-by-step explanation:
We are told that now Randy is four years older than Eric:
[tex]R=E+4[/tex] (1)
Then, we are told that five years ago Randy was twice as old as Eric:
[tex]R-5=2(E-5)[/tex] (2)
At this point we have a system with two equations and two unknowns.
Let's begin by substituting (1) in (2):
[tex]E+4-5=2(E-5)[/tex] (3)
[tex]E+4-5=2E-10[/tex] (4)
Isolating [tex]E[/tex]:
[tex]E=9[/tex] (5) This is Eric's current age
Substituting (5) in (1):
[tex]R=9+4[/tex] (6)
[tex]R=13[/tex] (7) This is Randy's current age
This means that five years ago Randy's age was 8 years old:
[tex]R-5=13-5=8[/tex]
