Question

At the snack bar, hot dogs cost $4 each and bottled water costs $2 each. In the first business hour of the day, less than $12 worth of hot dogs and water were sold. Which are reasonable solutions for this situation if x represents the number of hot dogs sold and y represents the number of bottles of water sold? Check all that apply. (–1, 5) (0, 6) (2, 1) (1, 1.5) (1, 3) (2, 2)

Answer 1

Answers:
(2,1)
(1,3)

Explanation:
Assume that the number of hot dogs is x and the number of water bottles is y.
We are given that:
1- cost of hot dog is $4
2- cost of water is $2
3- total profit was less than $12

This means that:
4x + 2y < 12

We will check the options that satisfy the above inequality:
Option 1: (-1,5):
This option is rejected as we cannot sell -1 hot dog

Option 2: (0,6):
4x + 2y = 4(0) + 2(6) = 12
12 is not less than 12
This option is incorrect

Option 3: (2,1):
4x + 2y = 4(2) + 2(1) = 8 + 2 = 10
10 is less than 12
This option is correct

Option 4: (1,1.5):
This option is incorrect as we cannot sell 1.5 bottle of water

Option 5: (1,3):
4x + 2y = 4(1) + 2(3) = 4 + 6 = 10
10 is less than 12
This option is correct

Option 6: (2,2):
4x + 2y = 4(2) + 2(2) = 8 + 4 = 12
12 is not less than 12
This option is incorrect

Hope this helps :)

Answer 2

Answer: The answers should be ( 2, 1)

(1, 3)