Kay buys one kilogram of chocolate cookies and two kilograms of almond cookies from Jean Jacques' bakery. Zach buys three kilograms of chocolate cookies and one kilogram of almond cookies. If Kay spends $11 on her cookies and Zach spends $18 on his, what is the price of one kilogram of chocolate cookies?

1 kg of chocolate cookies would cost $5.

Let C be the price of chocolate cookies and A be the cost of almond cookies. The equation for Kay's cookies would be

1C + 2A = 11.

The equation for Zach's cookies would be

3C+1A = 18.

Using Kay's equation, we will get C by itself:

1C+2A = 11

C+2A = 11

Subtract 2A from each side:

C+2A-2A = 11-2A

C=11-2A

Substitute this for C in Zach's equation:

3C+1A = 18

3 (11-2A) + 1A = 18

Use the distributive property:

3*11 - 3*2A + 1A = 18

33 - 6A + 1A = 18

Combine like terms:

33 - 5A = 18

Subtract 33 from each side:

33 - 5A - 33 = 18 - 33

-5A = - 15

Divide both sides by - 5:

-5A/-5 = - 15/-5

A = 3

Substitute this into Kay's equation:

C+2A = 11

C+2*3 = 11

C+6 = 11

Subtract 6 from both sides:

C+6-6 = 11-6

C=5