Answer:
Uncle is 34. Nephew is 10.
Step-by-step explanation:
Let u equal the age of the uncle, and n equal the age of the nephew.
First, two years ago, the sum of their ages was 40. We can represent this by subtracting 2 from each variable. Thus:
[tex](u-2)+(n-2)=40[/tex]
[tex]u+n-4=40[/tex]
[tex]u+n=44[/tex]
Next, in two years time, the uncle will be three times as old as his nephew. We can represent this by adding 2. Thus:
[tex]u+2=3(n+2)[/tex]
We now have a system of equations and can solve accordingly.
First, from the first equation, we can determine that:
[tex]u=44-n[/tex]
We can substitute this into the second equation.
[tex](44-n)+2=3(n+2)[/tex]
[tex]46-n=3n+6[/tex]
[tex]40=4n[/tex]
[tex]n=10[/tex]
Thus, the nephew's age is 10.
And the uncle's age is 44-10 or 34.
