Answer: Your brother is 15 years old right now.
Step-by-step explanation:
Let be "m" your currently age and "b" your brother's currently age.
Knowing that right now he is three times (this indicates multiplication) as old as you, you can write the following equation:
[tex]b=3m[/tex]
In five years your age will be:
[tex]m+5[/tex]
And your brother's age will be:
[tex]b+5[/tex]
Then, if in five years, your brother will be twice as old as you, you can set up the second equation:
[tex]b+5=2(m+5)[/tex]
Then, the System of equations is:
[tex]\left \{ {{b=3m} \atop {b+5=2(m+5)}} \right.[/tex]
Apply the Substitution method and substitute the first equation into the second one and solve for "m":
[tex]3m+5=2(m+5)\\\\3m+5=2m+10\\\\m=10-5\\\\m=5[/tex]
Substitute the value of "m" into the first equation and evaluate in order to find "b":
[tex]b=3(5)\\\\b=15[/tex]
