algebra word question

Question

a concession stand sells hot dogs for $2 and hamburgers for $3. one day 486 sandwiches were sold for a total of $1218. How many hot dogs were sold?

Answer 1

Hi Jacob,

 

Let

H = # hamburgers sold

D = # hot dogs sold

 

H + D = 486

3H + 2D = 1218

 

We can use elimination or substitution to solve

 

To use elimination, we need to multiply the first equation by -3.  This will eliminate the H

 

The first equation becomes

-3H - 3D = -1458

 3H + 2D =  1218

 

Adding these equations together, we have

-D = -240

and

D = 240

So 240 hot dogs were sold