Answer:
Ric is 7 years old.
Step-by-step explanation:
Choose variables for everyone's ages. I'll choose [tex]r[/tex] for Ric's age, [tex]p[/tex] for Paul's age, and [tex]t[/tex] for Tom's age.
Since Ric's age is half of Paul's age, we can write this equation:
[tex]r=\frac{1}{2}p[/tex]
Since Tom is two years younger than Paul, we can write this equation:
[tex]t=p-2[/tex]
Since the sum of all their ages is 33 years, we can write this equation:
[tex]r+p+t=33[/tex]
Since we know [tex]t[/tex] and [tex]r[/tex] in terms of [tex]p[/tex], we can replace them in the equation above as follows:
[tex]r+p+t=33\\(\frac{1}{2}p)+p+(p-2)=33[/tex]
Now we can solve for [tex]p[/tex] to find [tex]r[/tex] later:
[tex](\frac{1}{2}p)+p+(p-2)=33\\\frac{5}{2}p-2=33\\\frac{5}{2}p=35\\5p=70\\p=14[/tex]
Now that we know that [tex]p=14[/tex], we can substitute 14 for [tex]p\\[/tex] in the equation[tex]r=\frac{1}{2}p[/tex]:
[tex]r=\frac{1}{2}p\\r=\frac{1}{2}(14)\\r=7[/tex]
Ric is 7 years old.
