Question

Ric is half Paul's age. Tom is 2 years younger than Paul. The sum of all their ages is 33 years Show all working clearly to find Ric's age​

Answer 1

Answer:

Ric is 7 years old.

Step-by-step explanation:

Choose variables for everyone's ages. I'll choose $r$ for Ric's age, $p$ for Paul's age, and $t$ for Tom's age.

Since Ric's age is half of Paul's age, we can write this equation:

$r=\frac{1}{2}p$

Since Tom is two years younger than Paul, we can write this equation:

$t=p-2$

Since the sum of all their ages is 33 years, we can write this equation:

$r+p+t=33$

Since we know $t$ and $r$ in terms of $p$, we can replace them in the equation above as follows:

$r+p+t=33\\(\frac{1}{2}p)+p+(p-2)=33$

Now we can solve for $p$ to find $r$ later:

$(\frac{1}{2}p)+p+(p-2)=33\\\frac{5}{2}p-2=33\\\frac{5}{2}p=35\\5p=70\\p=14$

Now that we know that $p=14$, we can substitute 14 for $p$ in the equation$r=\frac{1}{2}p$:

$r=\frac{1}{2}p\\r=\frac{1}{2}(14)\\r=7$

Ric is 7 years old.