Let's refer to the chocolate cookies using the variable c, and the oatmeal cookies using the variable o.
Using the information we have, we can set up two equations for the two different transactions.
4c + 9o = 126
8c + 5o = 122
Now, we need to solve for one of the variables in the first equation. I will solve for o.
4c + 9o = 126
9o = 126 - 4c
o = 14 - 4/9c
Next, we'll take this value for o and plug it into the second equation for the variable o. Then we can solve for c.
8c + 5(14 - 4/9c) = 122
8c + 70 - 2 2/9c = 122
5 7/9c + 70 = 122
5 7/9c = 52
c = 9
Finally, we can use the value of c and plug it back into the first equation to solve for o.
o = 14 - 4/9(9)
o = 14 - 4
o = 10
1 dozen chocolate cookies costs $9
1 dozen oatmeal cookies costs $10
Hope this helps!