Question

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? Explain using equations. Are they able to get 12 sandwiches for $85?

Answer 1

First setup the system of equations for the given case.
Let sandwich=x
and delivery fee =y
Equations are:
4x+y=33 Equation 1
8x+y=61 Equation 2
Subtract equation 1 from 2.
4x=28
x=7
Now substitute value of x in equation 1.
4(7)+y=33
28+y=33
y=5

So cost of single sandwich=$7 and Delivery fee=$5

Now cost of  12 sandwiches:
12x+y=85
Put y=5
12x+5=85
12x=80
x=6.67 which is less than 7. So, They are not able to get 12 sandwiches for $85.