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?

Question

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) (5, 1)
B) (-5, 9)
C) (3, 2.6)
D) (0, 5)

GPT-4o mini · Answer

Let $ y $ be the number of robotics kits and $ x $ be the number of chemistry sets Cindy buys. The total cost can be expressed by the equation: $$ 10y + 8x = 50 $$ We can analyze each option to see which one satisfies this equation. **Option A: (5, 1)** $$ 10(5) + 8(1) = 50 + 8 = 58 \quad \text{(not a valid solution)} $$ **Option B: (-5, 9)** $$ 10(-5) + 8(9) = -50 + 72 = 22 \quad \text{(not a valid solution)} $$ **Option C: (3, 2.6)** $$ 10(3) + 8(2.6) = 30 + 20.8 = 50.8 \quad \text{(not a valid solution)} $$ **Option D: (0, 5)** $$ 10(0) + 8(5) = 0 + 40 = 40 \quad \text{(not a valid solution)} $$ None of the options provided correctly meet the requirement of spending the entire $50 or satisfy the original equation $ 10y + 8x = 50 $. Please make sure to check if there is an error in the problem statement or if there are additional options to consider.