While in a store, your father purchases drinks for 6 people. Part of your family wants coffee and the rest want a soda. Coffee cost $.49 per cup and sodas are $1.29 each. The cost of the drinks before tax was $6.14.
(a).Write a mathematical model that represents the total # cost of cups of coffee & sodas.
(b). Write a mathematical model to represent the cost of coffee & soda.
(c).Solve the system of equations using the elimination method.

Question

While in a store, your father purchases drinks for 6 people. Part of your family wants coffee and the rest want a soda. Coffee cost $.49 per cup and sodas are $1.29 each. The cost of the drinks before tax was $6.14. 
(a).Write a mathematical model that represents the total # cost of cups of coffee & sodas. 
(b). Write a mathematical model to represent the cost of coffee & soda. 
(c).Solve the system of equations using the elimination method.

anonymous · Answer

Let c and s be the number of coffee cups and sodas respectively.  $ will be expressed as pennies.

Solve the following for c and s:

c+s=6
49c+129s=614

c=6-s
49(6-s)+129s=614 //Expand
294 + 80 s = 614
80 s = 320
s=4

c=6-4
c=2