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?(1 point)

Question

Responses

(−5,9)
left parenthesis negative 5 comma 9 right parenthesis

(5,1)
left parenthesis 5 comma 1 right parenthesis

(3,2.6)
left parenthesis 3 comma 2.6 right parenthesis

(0,5)

Answer 1

To determine if the solutions are viable, we can set up the equation based on Cindy's total budget:

Let:

• \( y \) = number of robotics kits
• \( x \) = number of chemistry sets

The equation based on the total spent is: \[ 10y + 8x = 50 \]

Now, we can check each of the provided options to see if they satisfy this equation.

1. For \((-5, 9)\): \[ 10(-5) + 8(9) = -50 + 72 = 22 \quad (\text{Not valid}) \]

2. For \((5, 1)\): \[ 10(5) + 8(1) = 50 + 8 = 58 \quad (\text{Not valid}) \]

3. For \((3, 2.6)\): \[ 10(3) + 8(2.6) = 30 + 20.8 = 50.8 \quad (\text{Not valid}) \]

4. For \((0, 5)\): \[ 10(0) + 8(5) = 0 + 40 = 40 \quad (\text{Not valid}) \]

Therefore, none of the provided options are viable solutions for the number of robotics kits and chemistry sets Cindy can purchase while spending her entire $50.