Quess and Check problem Using Algebra NOT guess and check

Question

Jackie ordered sandwiches for her friends. The veggie sandwiches cost $7 apiece and the meat sandwiches cost $5 apiece. Jackie ordered 7 sandwiches and paid $45. How many of each type of sandwich did she order?

 

I don't understand how to set this up as a solvable equation.

I'm doing 7n+5n=45 which is not working? What am I doing wrong???

 

How to I set up this type of problem? Thanks

Answer 1

ANSWER: Two meat sandwiches and 5 Veggie sandwiches

 

x=number of veggie sandwiches

y=number of meat sandwiches

 

7x+5y=45; this is the total cost of the sandwiches

x+y=7; this is the total number of the sandwiches given in the problem

 

Now you have a system of equations. You can solve by substitution or elimination. I will use substitution and solve the second equation for x. Therefore, x=7-y

 

Now substitute that value of x into the first equation and solve for y. 

 

7(7-y)+5y=45

49-7y+5y=45

4=2y

y=2

 

Now plug the value of y into either equation and solve for x. I will use the second equation.

 

x+2=7

x=5

 

So there were 2 meat sandwiches and 5 veggie sandwiches.