Question

Dan and Mario went to a sandwich shop to buy sandwiches for their group of friends. Dan bought 2 tuna and 5 vegetarian sandwiches for $37. Mario bought 4 tuna and 3 vegetarian sandwiches for $39. Which system of equations can be used to solve for the cost of each kind of sandwich

Answer 1

2t+5v=37 and 4t+3v=39

Solve the first for t

t=18.5-2.5v and use this t in the second equation...

4(18.5-2.5v)+3v=39

74-10v+3v=39

-7v=-35

v=$5.00 and since t=18.5-2.5v

t=$6.00

So tuna sandwiches cost $6.00 and vegetarian sandwiches cost $5.00.

Answer 2

`2x+5y= 37`

`4x+3y= 39`

Explanation:

Given : Dan bought 2 tuna and 5 vegetarian sandwiches for $37. Mario bought 4 tuna and 3 vegetarian sandwiches for $39.

To Find: Which system of equations can be used to solve for the cost of each kind of sandwich

Solution:

Let the cost of 1 tuna be x

Cost of 2 tuna = 2x

Cost of 4 tuna = 4x

Let the cost of 1 vegetarian sandwich be y

Cost of 5 sandwiches= 5y

Cost of 3 sandwiches= 3y

Since we are given that Dan bought 2 tuna and 5 vegetarian sandwiches for $37

So, equation becomes:
`2x+5y= 37`

Mario bought 4 tuna and 3 vegetarian sandwiches for $39.

So, equation becomes:
`4x+3y= 39`

Hence system of equations can be used to solve for the cost of each kind of sandwich :

`2x+5y= 37`

`4x+3y= 39`