Question

10) At a store, six bottles of soda and two bags of chips cost $11.50. Three bottles of soda and four bags of chips cost $11.75. a) Write a system of equations using b as the cost of one bottle of soda and c as the cost of one bag of chips. b) Use elimination or substitution method to determine b and c for this situation. You MUST show all your work for full credit!​

Answer 1

Answer: a) The system of equations is:

6b + 2c = 11.50

3b + 4c = 11.75

b) Using the elimination method:

Multiply the first equation by -2:

-12b - 4c = -23

Add the second equation to this equation:

-9b = -11.25

Divide both sides by -9:

b = 1.25

Substitute b = 1.25 into one of the original equations:

6(1.25) + 2c = 11.50

Simplify and solve for c:

7.50 + 2c = 11.50

2c = 4

c = 2

Therefore, one bottle of soda costs $1.25 and one bag of chips costs $2.

Explanation: