Answer: Hotdog buns: 8 packages, Hamburger buns: 4 packages
Explaination: While reading the problem, let's take some notes here. We have two different types of buns. Let's name the hotdog buns as x and the hamburger buns as y. So just by doing that we can come up with the equation: x + y = 12 (12 is the total packages of buns). Next we know that the Harlin family has bought 20$ worth of buns (since each family contributed 20$ and the Harlin family is a family). That gives another equation which is: 1.5x + 2y = 20. Now you treat it as a system of equations.
x + y = 12
1.5x + 2y =20
I'm going to quickly solve it (sorry I won't explain how I do this, but ask if you want me to)
-2x + -2y = -24
1.5x +2y = 20
-.5x = -4
x = 8
8 + y =12
y = 4.