Question

A cafeteria sells sandwiches and chips. They earn $1 for each bag of chips sold and $6 profit for each sandwich sold. They sell 50 items in total for a profit of $115.

Solve the systems of equations. Show all steps.

How many sandwiches did they sell? How many bags of chips?

Answer 1

Answer : 13 sandwiches, 37 bags of chips

Step by step:
Lets say that chips are x and sandwiches are y.
x+y=50
1x+6y=115
That’s the same as...
x+y=50
x+6y=115
To solve by elimination, lets multiply the top equation by -1 so that we can cancel out x.
-1(x+y=50)
x+6y=115

-x-y=-50
x+6y=115
Now eliminate the x’s and solve for y
-y=-50
6y=115
(-y+6y=5y, -50+115=65)

5y=65
(divide by 5)
y=13

Now plug y=13 into one of the original equations. Lets use x+y=50.
x+13=50
(subtract 13 from both sides)
x=37

(37, 13)