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

Choose One Of The Following 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 which solution is viable, we can use the following equations based on Cindy's spending:

Let \( y \) be the number of robotics kits and \( x \) be the number of chemistry sets. The cost equation based on her winnings is:

\[ 10y + 8x = 50 \]

Now, let’s evaluate each of the given points to see if they satisfy the equation:

1. (−5, 9):

   • \( 10(-5) + 8(9) = -50 + 72 = 22 \) (not equal to 50)

2. (5, 1):

   • \( 10(5) + 8(1) = 50 + 8 = 58 \) (not equal to 50)

3. (3, 2.6):

   • \( 10(3) + 8(2.6) = 30 + 20.8 = 50.8 \) (not equal to 50)

4. (0, 5):

   • \( 10(0) + 8(5) = 0 + 40 = 40 \) (not equal to 50)

None of the points provided satisfy the equation \( 10y + 8x = 50 \). Therefore, none of the options given are viable solutions with the information provided.