Cindy won $50.00 for getting first place in the Science Fair. She spent her winnings on robotics kits and chemistry sets. Each robotics kit (y) costs $10.00, while each chemistry set costs $8.00 (x). Which of the following is a viable solution to the number of robotics kits and chemistry sets Cindy can purchase, assuming she spends her entire winnings?
A. (0,5)
B. (3,2.6)
C. (5, 1)
D. (-5, 9)
To find which of the given solutions is viable, we need to determine if the total cost of the purchases equals $50.00.
Let's calculate the total cost for each option:
A. (0,5)
Chemistry sets = 5
Robotics kits = 0
Total cost = (0 * $10) + (5 * $8) = $40
This is not equal to $50, so option A is not viable.
B. (3,2.6)
Chemistry sets = 2.6
Robotics kits = 3
Total cost = (3 * $10) + (2.6 * $8) = $30 + $20.8 = $50.8
This is not equal to $50, so option B is not viable.
C. (5,1)
Chemistry sets = 1
Robotics kits = 5
Total cost = (5 * $10) + (1 * $8) = $50
This is equal to $50, so option C is a viable solution.
D. (-5,9)
This option includes a negative number of robotics kits, which is not possible in this context since Cindy cannot purchase a negative number of kits. Therefore, option D is not viable.
In conclusion, the only viable solution is C. (5, 1), which means Cindy can purchase 5 robotics kits and 1 chemistry set.