solve the below problem

Question

A vendor sells hot dogs and bags of potato chips. A customer buys 4 hot
dogs and 5 bags of potato chips for $12.00. Another customer buys 3 hot
dogs and 4 bags of potato chips for $9.25. Find the cost of each item.

please include full work

Answer 1

Let h = price of hotdogs

Let c = price of chips

 

4h + 5c = 12

3h + 4c = 9.25

 

Let's eliminate a variable.  Multiply 1st equation by 3,

multiply 2nd equation by -4, then add the resulting equations

 

 12h + 15c = 36

-12h - 16c = -37

---------------------

         -c = -1

          c = $1

 

Substitute the value 1 into one of the original equations for c

and solve for h

 

 
4h + 5c = 12

4h + 5 = 12

4h = 7

h = $1.75

 

Bag of potato chips cost $1

Hot dogs cost $1.75