Q:

3 groups of students went to the burger barn for a study break and snack. the first group ordered 4 burgers, 5 fries, and 7 drinks for $25.60. the second group ordered 8 burgers, 5 fries, and 6 drinks for $37.90. the third group ordered 12 burgers, 10 fries, and 11 drinks for $61.30. suppose we want to find the cost of a burger, fries, and a drink. a) define variables for setting up a system of equations. b) write the system of equations that will solve the problem. use the variables from part a. c) what is the cost of a burger, an order of fries, and a drink. give in sentence form.

Accepted Solution

A:
Answer:Cost of one burger, a = $3.35Cost of one fries, b = $0.9Cost of one drink, c = $1.1Step-by-step explanation:Leta be cost of one burgerb be the cost of on fryc be the cost of on drinkSo for the 1st group, 4a+5b+7c = $25.60     -----------(1)      for the 2st group, 8a+5b+6c = $37.90     ----------(2)      for the3st group, 12a+10b+11c = $61.30    ----------(3)Now solving (1) and (2)That is (1) x 2 - (2) gives,5b+8c = 13.80 ----------------------(4)Now, (1) x 3 - (3), we get5b+10c = 15.5    ---------------------(5)Solving (4) and (5), we get c = 1.1Now putting c in equation (4), we getb = 0.9Now from (1), we get4a+5b+7c = $25.604a+5(0.9)+7(1.1) = $25.60a = 3.35Cost of one burger, a = $3.35Cost of one fries, b = $0.9Cost of one drink, c = $1.1