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?(1 point)
Responses

(0,5)
left parenthesis 0 comma 5 right parenthesis

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

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

(5,1)

Answer 1

To determine which of the provided options is a viable solution for how many robotics kits (y) and chemistry sets (x) Cindy can purchase with her $50 winnings, we can set up the equation based on the costs:

Let \( x \) be the number of chemistry sets and \( y \) be the number of robotics kits.

The total cost equation is:
\[ 10y + 8x = 50 \]

Now, we can evaluate each option to see if it satisfies the equation:

1. **(0, 5)**:
- \( x = 0 \), \( y = 5 \)
- Total cost: \( 10(5) + 8(0) = 50 + 0 = 50 \) (Valid)

2. **(−5, 9)**:
- \( x = -5 \), \( y = 9 \)
- Total cost: \( 10(9) + 8(-5) = 90 - 40 = 50 \) (Invalid because x cannot be negative)

3. **(3, 2.6)**:
- \( x = 3 \), \( y = 2.6 \)
- Total cost: \( 10(2.6) + 8(3) = 26 + 24 = 50 \) (Invalid because y cannot be a fraction)

4. **(5, 1)**:
- \( x = 5 \), \( y = 1 \)
- Total cost: \( 10(1) + 8(5) = 10 + 40 = 50 \) (Valid)

Out of these options, the viable solutions are:

- (0, 5)
- (5, 1)

Thus, both (0, 5) and (5, 1) are valid. If only one option must be chosen, you can select either option as a correct answer, with a preference for the first one if only one selection is required.