Let current age of Adam = x years
Let current age of Brianna = y years
Question says that "Adam is now 9 years older than Brianna "
Which means x=y+9 ...(i)
To find the age 13 years ago, we just subtract 13 from age of each person.
Age of Adam before 13 years = (x-13) years
Age of Brianna before 13 years = (y-13) years
Question says that "13 years ago he was twice as old as she was then"
Which means (x-13)=2(y-13) ...(ii)
plug value of x from equation (i) into (ii)
(x-13)=2(y-13)
(y+9-13)=2(y-13)
y-4=2y-26
y-2y=-26+4
-y=-22
y=22
plug value of y=22 into equation (i)
x=y+9 = 22+9 = 31
Hence Adam is 31 years old and Brianna is 22 years old.
