Answer:
Ric is 7 years old.
Step-by-step explanation:
Choose variables for everyone's ages. I'll choose
for Ric's age,
for Paul's age, and
for Tom's age.
Since Ric's age is half of Paul's age, we can write this equation:
![r=\frac{1}{2}p](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B1%7D%7B2%7Dp)
Since Tom is two years younger than Paul, we can write this equation:
![t=p-2](https://tex.z-dn.net/?f=t%3Dp-2)
Since the sum of all their ages is 33 years, we can write this equation:
![r+p+t=33](https://tex.z-dn.net/?f=r%2Bp%2Bt%3D33)
Since we know
and
in terms of
, we can replace them in the equation above as follows:
![r+p+t=33\\(\frac{1}{2}p)+p+(p-2)=33](https://tex.z-dn.net/?f=r%2Bp%2Bt%3D33%5C%5C%28%5Cfrac%7B1%7D%7B2%7Dp%29%2Bp%2B%28p-2%29%3D33)
Now we can solve for
to find
later:
![(\frac{1}{2}p)+p+(p-2)=33\\\frac{5}{2}p-2=33\\\frac{5}{2}p=35\\5p=70\\p=14](https://tex.z-dn.net/?f=%28%5Cfrac%7B1%7D%7B2%7Dp%29%2Bp%2B%28p-2%29%3D33%5C%5C%5Cfrac%7B5%7D%7B2%7Dp-2%3D33%5C%5C%5Cfrac%7B5%7D%7B2%7Dp%3D35%5C%5C5p%3D70%5C%5Cp%3D14)
Now that we know that
, we can substitute 14 for
in the equation
:
![r=\frac{1}{2}p\\r=\frac{1}{2}(14)\\r=7](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B1%7D%7B2%7Dp%5C%5Cr%3D%5Cfrac%7B1%7D%7B2%7D%2814%29%5C%5Cr%3D7)
Ric is 7 years old.