a sandwich store charges a delivery fee to bring lunch to an office building. one office pays $33 for 4 turkey sandwiches. another office pays $61 for 8 turkey sandwiches. how much does each turkey sandwich add to the cost of the delivery fee? explain using equations and graph. are they able to get 12 sandwiches for $85?

Let each turkey sandwich cost x, and the fixed delivery fee be y.
From the first situation, 4x + y = 33
From the second case with 8 sandwiches, 8x + y = 61
Subtracting the first equation from the second gives 4x = 28
x = 7
Substituting this back into the first equation gives y = 5.
Therefore, each turkey sandwich costs $7 and the delivery fee is $5.
If you were to have 12 turkey sandwiches delivered, the cost would be 12x + y = 12*7 + 5 = $89, so this would be more than $85.

If you want to do it graphically, convert both equations into slope-intercept form.
y = -4x + 33 and y = -8x + 61
For the first equation, the y-intercept is (0,33) and the x-intercept is (33/4, 0).
For the second equation, the y-intercept is (0,61) and the x-intercept is (61/8, 0).
Connect the intercepts for each equation, then find the point of intersection. The x- and y-coordinates of the point of intersection are x = 7 and y = 5, which are the values that will solve the equations.