Expert: Scott A Wilson - 9/9/2010

Question
A hamburger costs 30 cents more than a hot dog and 20 cents less than a cheeseburger. If 3 hamburgers cost 75 cents less than 2 hot dogs and 2 cheeseburgers, how much does a hamburger cost?  

Answer
Let x = hamburger price, y = hot dog price, and z = cheeseburger price.  We are given that x = y + 30 and x = z - 20.
We are also given 3x + 75 = 2y + 2z.

Here are 3 equations and 3 unknowns that can be solved to determine the values for x, y, and z.

I would take x = 30 + y and note that y = x - 30.
I would also take x = z - 20 and solve for z, getting z = x + 20.

Putting this in 3x + 75 = 2y + 2z for y and z would given an expressionh with only x.  This can be solved for x.
Once this is known, y and z can be found using y = x - 30 and
z = x + 20.

Note the expressions all are cents.  
So this can be said to make cents as well as make sense, right?