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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​

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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.

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