Answer:
11 years old
Step-by-step explanation:
If four brothers have the average age 6, then the sum of their ages is
[tex]4\cdot 6=24[/tex]
years.
Let x years be the age of sister. If four brothers and their sister have the average age 7, then
[tex]\dfrac{24+x}{5}=7.[/tex]
Multiply this equation by 5:
[tex]24+x=35\Rightarrow x=35-24=11.[/tex]
The sister is 11 years old.
