Develop an equation for the problem

Question

At your class picnic, you volunteer to grill hot dogs. The hot dogs come in packages of 8, and the hot dog buns come in packages of 6. After everyone is finished eating, you have an open package of hot dogs that contain 2 hot dogs and an open package of hot dog buns that contains 4 buns. How many hot dogs were eaten? Develop an equation for the problem.

Answer 1

I have not been able to develop an equation. The problem gives two variables - number of hot dog packages, and number of bun packages. Two variable require two equations.

 

A solution came be determined with some reasoning.

The number of hot dogs is always six more than a multiple of 8: 14, 22, 30, 38, ...

The number of buns is always two more than a multiple of 6: 8, 14, (a ha, there it is!)

 

14 hot dogs and 14 buns were eaten.