Davis's Bakery sold one customer 4 dozen chocolate cookies and 9 dozen oatmeal cookies for $103. The bakery also sold another customer 4 dozen chocolate cookies and 2 dozen oatmeal cookies for $54. How much do each kind of cookie cost per dozen?
Let x be the price per dozen of chocolate cookies.
Let y be the price per dozen of oatmeal cookies.
For the first customer 4x + 9y = 103.
For the second customer 4x + 2y = 54.
We can multiply the second customer's equation by 4 to eliminate the 4x term: 16x + 8y = 216
Multiply the first customer's equation by -2. There are no coefficients of x that match up when we subtractthe equations, so we will have to multiply through by 8 to make -8x a multiple of 16x: -8x - 18y = -206
So the first equation is:
-8x - 18y + 16x + 8y = -206 + 216
8x - 10y = 10
Now we can add the equations: 16x + 8y = 216 + 10 or 16x + 8y = 226.
8x - 10y = 10
18x = 236
x = <<13=13>>13
Then y = (54 - 4 * 13) / 2 = (54 - 52) / 2 = 1
Thus, the price per dozen of chocolate cookies is $<<13=13>>13, and the price per dozen of oatmeal cookies is $<<1=1>>1. Answer: \boxed{13, 1}.