Question

A deli has two platters of sandwiches. The first platter costs ​$54 and you get 2 roast beef sandwiches and 5 ham sandwiches. The other platter costs ​$59 and you get 5 roast beef sandwiches and 3 ham sandwiches. Let x represent the cost of each roast beef sandwich and y represent the cost of each ham sandwich. What is the system of linear equations for the given​ scenario? What is the cost of each​ sandwich? I just need to know how much each sandwich costs

Answer 1

Cost of each roast beef sandwich = $7

Cost of each ham sandwich = $8

Explanation:

x = cost of each roast beef sandwich

y = cost of each ham sandwich

2x + 5y = 54 (1)

5x + 3y = 59 (2)

Multiply (1) by 5 and (2) by 2

10x + 25y = 270

10x + 6y = 118

Subtract to eliminate x

25y - 6y = 270 - 118

19y = 152

Divide both sides by 19

y = 152 / 19

= 8

y = $8

Substitute y = 8 into (1)

2x + 5y = 54 (1)

2x + 5(8) = 54

2x + 40 = 54

2x = 54 - 40

2x = 14

x = 14 / 2

x = $7

Cost of each roast beef sandwich = $7

Cost of each ham sandwich = $8