A deli has two platters of sandwiches. The first platter costs 46 dollars and you get 2 roast beef sandwiches and 5 ham sandwiches. The other platter costs 58 dollars 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 given for this problem? What is the cost of each sandwich?
Roast beef sandwhich:
7$
Ham sandwhich:
8$
Step-by-step 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
