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

(3,2.6)

left parenthesis 3 comma 2.6 right parenthesis
(5,1)
left parenthesis 5 comma 1 right parenthesis
(0,5)
left parenthesis 0 comma 5 right parenthesis
(−5,9)

Answer 1

To determine a viable solution to the number of robotics kits and chemistry sets Cindy can purchase, we can set up the equation based on her total spending:

Let:

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

The cost equation based on her total winnings is:

\[ 10y + 8x = 50 \]

Now we can evaluate each of the provided options:

1. \( (3, 2.6) \):

   • Substitute \( y = 3 \) and \( x = 2.6 \):
   • \( 10(3) + 8(2.6) = 30 + 20.8 = 50.8 \) (not viable)

2. \( (5, 1) \):

   • Substitute \( y = 5 \) and \( x = 1 \):
   • \( 10(5) + 8(1) = 50 + 8 = 58 \) (not viable)

3. \( (0, 5) \):

   • Substitute \( y = 0 \) and \( x = 5 \):
   • \( 10(0) + 8(5) = 0 + 40 = 40 \) (not viable)

4. \( (-5, 9) \):

   • Substitute \( y = -5 \) and \( x = 9 \):
   • \( 10(-5) + 8(9) = -50 + 72 = 22 \) (not viable)

None of the given options satisfy the equation \( 10y + 8x = 50 \).

Thus, the correct answer is that none of the provided options are viable solutions given the spending conditions.