A survey is given to adults in each family. $a$ is the age of the adult,and $b$ is the age of the oldest child - these are recorded. The ages of the oldest child are summarized in the following box and whisker diagram:
The regression line of $a$ on $b$ is $a = 7/4b+20$, and the regression line of $b$ on $c$ is $b = 1/2a-9$
Find the mean age of all the adults surveyed.
I tried solving the system of equations for $a$ and $b$, which gives me $a = 34, b = 8$. Meaning (I guess) that the average age of the adults is 34, isn't it? Because the answer is wrong according to my teacher, but he doesn't explain me why.